Journal articles on the topic 'Einstein-type structure'
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Chen, Xiaomin. "Einstein-Weyl structures on trans-Sasakian manifolds." Mathematica Slovaca 69, no. 6 (December 18, 2019): 1425–36. http://dx.doi.org/10.1515/ms-2017-0319.
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Abstract In this article we study Einstein-Weyl structures on a 3-dimensional trans-Sasakian manifold M of type (α, β). First, we prove that a 3-dimensional trans-Sasakian manifold admitting both Einstein-Weyl structures W± = (g, ±θ) is Einstein, or is homothetic to a Sasakian manifold if α ≠ 0. Next for β ≠ 0 it is proved that M is Einstein, or is homothetic to an f-Kenmotsu manifold if it admits an Einstein-Weyl structure W = (g, κη) for some nonzero constant κ. Finally, a classification is obtained when a trans-Sasakian manifold admits a closed Einstein-Weyl structure. Further, if M is compact we also obtain two corollaries.
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Manev, Hristo, and Mancho Manev. "Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure." Mathematics 9, no. 14 (July 20, 2021): 1704. http://dx.doi.org/10.3390/math9141704.
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We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements.
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CALVARUSO, G., and D. PERRONE. "HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES." Journal of the Australian Mathematical Society 88, no. 3 (May 12, 2010): 323–37. http://dx.doi.org/10.1017/s1446788710000157.
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AbstractWe prove that all g-natural contact metric structures on a two-point homogeneous space are homogeneous contact. The converse is also proved for metrics of Kaluza–Klein type. We also show that if (M,g) is an Einstein manifold and $\tilde G$ is a Riemannian g-natural metric on T1M of Kaluza–Klein type, then $(T_1 M,\tilde \eta ,\tilde G)$ is H-contact if and only if (M,g) is 2-stein, so proving that the main result of Chun et al. [‘H-contact unit tangent sphere bundles of Einstein manifolds’, Q. J. Math., to appear. DOI: 10.1093/qmath/hap025] is invariant under a two-parameter deformation of the standard contact metric structure on T1M. Moreover, we completely characterize Riemannian manifolds admitting two distinct H-contact g-natural contact metric structures, with associated metric of Kaluza–Klein type.
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Wang, Changliang. "Stability of Riemannian manifolds with Killing spinors." International Journal of Mathematics 28, no. 01 (January 2017): 1750005. http://dx.doi.org/10.1142/s0129167x17500057.
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Riemannian manifolds with nonzero Killing spinors are Einstein manifolds. Kröncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in [Stable and unstable Einstein warped products, preprint (2015), arXiv:1507.01782v1 ]. In this paper, we obtain a new proof for this stability result by using a Bochner-type formula in [X. Dai, X. Wang and G. Wei, On the stability of Riemannian manifold with parallel spinors, Invent. Math. 161(1) (2005) 151–176; M. Wang, Preserving parallel spinors under metric deformations, Indiana Univ. Math. J. 40 (1991) 815–844]. Moreover, existence of real Killing spinors is closely related to the Sasaki–Einstein structure. A regular Sasaki–Einstein manifold is essentially the total space of a certain principal [Formula: see text]-bundle over a Kähler–Einstein manifold. We prove that if the base space is a product of two Kähler–Einstein manifolds then the regular Sasaki–Einstein manifold is unstable. This provides us many new examples of unstable manifolds with real Killing spinors.
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Al-Solamy, Falleh, Jeong-Sik Kim, and Mukut Tripathi. "On η-Einstein Trans-Sasakian Manifolds." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (January 1, 2011): 417–40. http://dx.doi.org/10.2478/v10157-011-0036-x.
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On η-Einstein Trans-Sasakian ManifoldsA systematic study of η-Einstein trans-Sasakian manifold is performed. We find eight necessary and sufficient conditions for the structure vector field ζ of a trans-Sasakian manifold to be an eigenvector field of the Ricci operator. We show that for a 3-dimensional almost contact metric manifold (M,φ, ζ, η, g), the conditions of being normal, trans-K-contact, trans-Sasakian are all equivalent to ∇ζ ∘ φ = φ ∘ ∇ζ. In particular, the conditions of being quasi-Sasakian, normal with 0 = 2β = divζ, trans-K-contact of type (α, 0), trans-Sasakian of type (α, 0), andC6-class are all equivalent to ∇ ζ = -αφ, where 2α = Trace(φ∇ζ). In last, we give fifteen necessary and sufficient conditions for a 3-dimensional trans-Sasakian manifold to be η-Einstein.
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Balan, Vladimir. "Synge-Beil and Riemann-Jacobi jet structures with applications to physics." International Journal of Mathematics and Mathematical Sciences 2003, no. 27 (2003): 1693–702. http://dx.doi.org/10.1155/s0161171203211145.
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In the framework of geometrized first-order jet approach, we study the Synge-Beil generalized Lagrange jet structure, derive the canonic nonlinear and Cartan connections, and infer the Einstein-Maxwell equations with sources; the classical ansatz is emphasized as a particular case. The Lorentz-type equations are described and the attached Riemann-Jacobi structures for two certain uniparametric cases are presented.
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Friedrich, Helmut. "Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times." Journal of Geometry and Physics 17, no. 2 (October 1995): 125–84. http://dx.doi.org/10.1016/0393-0440(94)00042-3.
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Boyer, Charles P. "Contact Structures of Sasaki Type and Their Associated Moduli." Complex Manifolds 6, no. 1 (January 1, 2019): 1–30. http://dx.doi.org/10.1515/coma-2019-0001.
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Abstract This article is based on a talk at the RIEMain in Contact conference in Cagliari, Italy in honor of the 78th birthday of David Blair one of the founders of modern Riemannian contact geometry. The present article is a survey of a special type of Riemannian contact structure known as Sasakian geometry. An ultimate goal of this survey is to understand the moduli of classes of Sasakian structures as well as the moduli of extremal and constant scalar curvature Sasaki metrics, and in particular the moduli of Sasaki-Einstein metrics.
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Galaev, S. "On geometry of sub-Riemannian η-Einstein manifolds." Differential Geometry of Manifolds of Figures, no. 50 (2018): 68–81. http://dx.doi.org/10.5922/10.5922/0321-4796-2019-50-9.
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On a sub-Riemannian manifold of contact type a connection with torsion is considered, called in the work a Ψ-connection. A Ψ- connection is a particular case of an N-connection. On a sub-Riemannian manifold, a Ψ-connection is defined up to an endomorphism :DD of a distribution D, this endomorphism is called in the work the structure endomorphism. The endomorphism ψ is uniquely defined by the following relations: 0, (x, y) g( x, y), x, yD. If the distribution of a sub-Riemannian manifold is integrable, then the Ψ-connection is of the class of the quarter-symmetric connections. It is proved that the Ψ- connection is a metric connection if and only if the structure vector field of the sub-Riemannian structure is integrable. A formula expressing the Ψ-connections in terms of the Levi-Civita connection of the sub- Riemannian manifold is obtained. The components of the curvature tensors and the Ricci-tensors of the Ψ-connection and of the Levi-Civita connection are computed. It is proved that if a sub-Riemannian manifold is an η-Einstein manifold, then it is also an η-Einstein manifold with respect to the Ψ-connection. The converse holds true only under the condition that the trace of the structure endomorphism Ψ is a constant not depending on a point of the manifold. The paper is completed by the theorem stating that a Sasaki manifold is an η-Einstein manifold if and only if M is an η-Einstein manifold with respect to the Ψ-connection.
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Shima, Kazunari, and Motomu Tsuda. "On the structure of Einstein Hilbert-type action of the superon graviton model (SGM)." Classical and Quantum Gravity 19, no. 20 (September 26, 2002): 5101–11. http://dx.doi.org/10.1088/0264-9381/19/20/305.
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PRIETO, CARLOS TEJERO. "THE YANG–MILLS FUNCTIONAL AND BOGOMOLOV INEQUALITY FOR ARBITRARY PRINCIPAL BUNDLES OVER KÄHLER MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 08 (August 7, 2013): 1360015. http://dx.doi.org/10.1142/s0219887813600153.
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We study the Yang–Mills functional for principal fiber bundles with structure group a compact Lie group K over a Kähler manifold. In particular, we analyze the absolute minimizers for this functional and prove that they are exactly the Einstein K-connections. By means of the structure of the Yang–Mills functional at an absolute minimum, we prove that the characteristic classes of a principal K-bundle which admits an Einstein connection satisfy two inequalities. One of them is a generalization of the Bogomolov inequality whereas the other is an inequality related to the center of the structure group. Therefore, this way we offer a new and natural proof of the Bogomolov inequality that helps understanding its origin. Finally, in view of the Hitchin–Kobayashi correspondence we prove that every (poly-)stable principal Kℂ-bundle has to satisfy this generalized Bogomolov type inequality.
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Heller, Michael, Tomasz Miller, Leszek Pysiak, and Wiesław Sasin. "Geometry and general relativity in the groupoid model with a finite structure group." Canadian Journal of Physics 93, no. 1 (January 2015): 43–54. http://dx.doi.org/10.1139/cjp-2014-0145.
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In a series of papers (M. Heller et al. J. Math. Phys. 38, 5840 (1997). doi:10.1063/1.532186 ; M. Heller and W. Sasin. Int. J. Theor. Phys. 38, 1619 (1999). doi:10.1023/A:1026617913754 ; M. Heller et al. Int. J. Theor. Phys. 44, 619 (2005). doi:10.1007/s10773-005-3992-7 ) we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra, [Formula: see text], defined on a transformation groupoid Γ determined by the action of the Lorentz group on the frame bundle (E, πM, M) over space–time M. In the present work, we construct a simplified version of the gravitational sector of this model in which the Lorentz group is replaced by a finite group, G, and the frame bundle is trivial E = M × G. The model is fully computable. We define the Einstein–Hilbert action, with the help of which we derive the generalized vacuum Einstein equations. When the equations are projected to space–time (giving the “general relativistic limit”), the extra terms that appear due to our generalization can be interpreted as “matter terms”, as in Kaluza–Klein-type models. To illustrate this effect we further simplify the metric matrix to a block diagonal form, compute for it the generalized Einstein equations and find two of their “Friedman-like” solutions for the special case when G = [Formula: see text]. One of them gives the flat Minkowski space–time (which, however, is not static), another, a hyperbolic, linearly expanding universe.
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BISWAS, INDRANIL, and JOHN LOFTIN. "HERMITIAN–EINSTEIN CONNECTIONS ON PRINCIPAL BUNDLES OVER FLAT AFFINE MANIFOLDS." International Journal of Mathematics 23, no. 04 (April 2012): 1250039. http://dx.doi.org/10.1142/s0129167x12500395.
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Let M be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric g and a covariant constant volume form. Let G be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal G-bundle EG over M admits a Hermitian–Einstein structure if and only if EG is polystable. A polystable flat principal G-bundle over M admits a unique Hermitian–Einstein connection. We also prove the existence and uniqueness of a Harder–Narasimhan filtration for flat vector bundles over M. We prove a Bogomolov type inequality for semistable vector bundles under the assumption that the Gauduchon metric g is astheno-Kähler.
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Aerts, Diederik, and Lester Beltran. "Are Words the Quanta of Human Language? Extending the Domain of Quantum Cognition." Entropy 24, no. 1 (December 21, 2021): 6. http://dx.doi.org/10.3390/e24010006.
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In previous research, we showed that ‘texts that tell a story’ exhibit a statistical structure that is not Maxwell–Boltzmann but Bose–Einstein. Our explanation is that this is due to the presence of ‘indistinguishability’ in human language as a result of the same words in different parts of the story being indistinguishable from one another, in much the same way that ’indistinguishability’ occurs in quantum mechanics, also there leading to the presence of Bose–Einstein rather than Maxwell–Boltzmann as a statistical structure. In the current article, we set out to provide an explanation for this Bose–Einstein statistics in human language. We show that it is the presence of ‘meaning’ in ‘texts that tell a story’ that gives rise to the lack of independence characteristic of Bose–Einstein, and provides conclusive evidence that ‘words can be considered the quanta of human language’, structurally similar to how ‘photons are the quanta of electromagnetic radiation’. Using several studies on entanglement from our Brussels research group, we also show, by introducing the von Neumann entropy for human language, that it is also the presence of ‘meaning’ in texts that makes the entropy of a total text smaller relative to the entropy of the words composing it. We explain how the new insights in this article fit in with the research domain called ‘quantum cognition’, where quantum probability models and quantum vector spaces are used in human cognition, and are also relevant to the use of quantum structures in information retrieval and natural language processing, and how they introduce ‘quantization’ and ‘Bose–Einstein statistics’ as relevant quantum effects there. Inspired by the conceptuality interpretation of quantum mechanics, and relying on the new insights, we put forward hypotheses about the nature of physical reality. In doing so, we note how this new type of decrease in entropy, and its explanation, may be important for the development of quantum thermodynamics. We likewise note how it can also give rise to an original explanatory picture of the nature of physical reality on the surface of planet Earth, in which human culture emerges as a reinforcing continuation of life.
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Chang, Zhe, Zhi-Chao Zhao, Yong Zhou, and Qing-Hua Zhu. "Is there any relationship between glitches of Crab pulsar and Einstein-de Haas effect?" Monthly Notices of the Royal Astronomical Society 488, no. 1 (June 28, 2019): 1066–71. http://dx.doi.org/10.1093/mnras/stz1756.
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ABSTRACT Many pulsars show sudden rotation jumps, glitches, superimposed to the gradual rotation down due to the continued loss of energy by radiation. A lot of models have been proposed to explain glitches. Most of the models are associated with layer structure of neutron stars. We try to investigate possibility of relationship between glitches of Crab pulsar and Einstein-de Haas effect. In the scenarios, spin polarization of neutron matter with Skyrme-type interactions forms a macroscopic spin angular momentum, and the Einstein-de Haas effect – transfer between the macroscopic spin and orbit angular momentum – gives rise to glitches of pulsars. It is shown that the scenario is in agreement with the observations of Crab pulsar on glitches and post-glitches relaxation.
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Barreto, Adriano B., and Gilberto M. Kremer. "Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach." Symmetry 12, no. 7 (July 3, 2020): 1110. http://dx.doi.org/10.3390/sym12071110.
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The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed.
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Suh, Young, Pradip Majhi, and De Chand. "On mixed quasi-Einstein spacetimes." Filomat 32, no. 8 (2018): 2707–19. http://dx.doi.org/10.2298/fil1808707s.
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The object of the present paper is to study mixed quasi-Einstein spacetimes, briefly M(QE)4 spacetimes. First we prove that every Z Ricci pseudosymmetric M(QE)4 spacetimes is a Z Ricci semisymmetric spacetime. Then we study Z flat spacetimes. Also we consider Ricci symmetric M(QE)4 spacetimes and among others we prove that the local cosmological structure of a Ricci symmetricM(QE)4 perfect fluid spacetime can be identified as Petrov type I, DorO. We show that such a spacetime is the Robertson-Walker spacetime. Moreover we deal with mixed quasi-Einstein spacetimes with the associated generators U and V as concurrent vector fields. As a consequence we obtain some important theorems. Among others it is shown that a perfect fluid M(QE)4 spacetime of non zero scalar curvature with the basic vector field of spacetime as velocity vector field of the fluid is of Segr?e characteristic [(1,1,1),1]. Also we prove that a M(QE)4 spacetime can not admit heat flux provided the smooth function b is not equal to the cosmological constant k. This means that such a spacetime describe a universe which has already attained thermal equilibrium. Finally, we construct a non-trivial Lorentzian metric of M(QE)4.
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Zhang, Ai-Xia, Yan-Fang Jiang, and Ju-Kui Xue. "Nonlinear energy band structure of spin-orbit coupled Bose-Einstein condensates in optical lattice." Acta Physica Sinica 70, no. 20 (2021): 200302. http://dx.doi.org/10.7498/aps.70.20210705.
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<sec>In a recent experiment [Hamner C, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevLett.114.070401"> 2015 <i>Phys. Rev. Lett.</i> <b>114</b> 070401</ext-link>], spin-orbit coupled Bose-Einstein condensates in a translating optical lattice have been successfully prepared into any Bloch band, and directly proved to be the lack of Galilean invariance in the presence of the spin-orbit coupling. The energy band structure of the system becomes complicated because of the lack of Galilean invariance. At present, the energy band structure of the spin-orbit coupled Bose-Einstein condensates in optical lattice is still an open issue, especially the theoretical evidence for the in-depth understanding of the competition mechanism among the spin-orbit coupling, the Raman coupling, the optical lattice and the atomic interactions of the nonlinear energy band structure has not been clear yet.</sec><sec>In this paper, based on the two-mode approximation and variational analysis, the nonlinear energy band structure and current density of the spin-orbit coupled Bose-Einstein condensates in the one-dimensional optical lattice are investigated. We find that when the spin-orbit coupling, the Raman coupling, the optical lattice, and the atomic interactions satisfy certain conditions, a loop structure in the Brillouin zone edge will emerge. The critical condition for the loop structure emerging in the Brillouin zone edge is obtained in a parameter space. The Raman coupling and the optical lattice suppress the emergence of the loop structure, while the spin-orbit coupling and the atomic interactions promote the emerging of the loop structure and make the energy band structure more complex. Interestingly, the atomic interactions can make the loop structure occur at both the higher-lying bands and the lowest energy band. The energy band structure is closely related to the current density of the system. The spin-orbit coupling causes the current density to be strongly asymmetric and leads the current density distributions of different spin states to be separated from each other in the momentum space near the boundary of the Brillouin zone. The optical lattice strength and the Raman coupling can weaken the asymmetry. The appearance of loop structure breaks the Bloch oscillation and gives rise to the Landau-Zener tunneling. The separation of the current density distributions of different spin states in the momentum space means the emergence of the spin exchange dynamics. Our results are beneficial to the in-depth understanding of the nonlinear dynamics of the spin-orbit coupled Bose-Einstein condensates in optical lattice.</sec>
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Premoselli, Bruno. "A pointwise finite-dimensional reduction method for a fully coupled system of Einstein–Lichnerowicz type." Communications in Contemporary Mathematics 20, no. 06 (August 27, 2018): 1750076. http://dx.doi.org/10.1142/s0219199717500766.
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We construct non-compactness examples for the fully coupled Einstein–Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on the a priori pointwise asymptotic techniques of the [Formula: see text] theory.
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Kömürcü, Cihan, and Can Aktaş. "Investigation of the magnetized string distribution in the Marder universe with the cosmological term in f(R,T) theory." Modern Physics Letters A 35, no. 32 (August 20, 2020): 2050263. http://dx.doi.org/10.1142/s0217732320502636.
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In this study, we first obtained the cosmological term naturally in the Einstein–Hilbert type effect for the [Formula: see text] theory, then we discussed the magnetized string matter in the Marder universe, later the matter Lagrangian is not equivalent to string dust and we calculated independently for the string dust and the electromagnetic field, and added the magnetized string together. Finally, we studied the physical and geometric structure of the universe, limiting our results to some astrophysical observation data.
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Niedermaier, Max. "Nonstandard Action of Diffeomorphisms and Gravity’s Anti-Newtonian Limit." Symmetry 12, no. 5 (May 6, 2020): 752. http://dx.doi.org/10.3390/sym12050752.
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A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the lightcones to lines. Conventional tensors admit an analogous Anti-Newtonian limit, which however transforms according to a non-standard realization of the spacetime Diffeomorphism group. In addition to the type of the tensor the transformation law depends on, a set of integer-valued weights is needed to ensure the existence of a nontrivial limit. Examples are limiting counterparts of the metric, Einstein, and Riemann tensors. An adapted purely temporal notion of parallel transport is presented. By introducing a generalized Ehresmann connection and an associated orthonormal frame compatible with an invertible Carroll metric, the weight-dependent transformation laws can be mapped into a universal one that can be read off from the index structure. Utilizing this ‘decoupling map’ and a realization of the generalized Ehresmann connection in terms of scalar field, the limiting gravity theory can be endowed with an intrinsic Levi–Civita type notion of spatio-temporal parallel transport.
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Anastassiou, S., and I. Chrysikos. "Ancient solutions of the homogeneous Ricci flow on flag manifolds." Extracta Mathematicae 36, no. 1 (June 20, 2021): 99–145. http://dx.doi.org/10.17398/2605-5686.36.1.99.
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For any flag manifold M=G/K of a compact simple Lie group G we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions pass through an invariant Einstein metric on M, and by [13] they must develop a Type I singularity in their extinction finite time, and also to the past. To illustrate the situation we engage ourselves with the global study of the dynamical system induced by the unnormalized Ricci flow on any flag manifold M=G/K with second Betti number b2(M) = 1, for a generic initial invariant metric. We describe the corresponding dynamical systems and present non-collapsed ancient solutions, whose α-limit set consists of fixed points at infinity of MG. Based on the Poincaré compactification method, we show that these fixed points correspond to invariant Einstein metrics and we study their stability properties, illuminating thus the structure of the system’s phase space.
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Ni, Wei-Tou. "Equivalence principles, spacetime structure and the cosmic connection." International Journal of Modern Physics D 25, no. 04 (March 10, 2016): 1630002. http://dx.doi.org/10.1142/s0218271816300020.
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After reviewing the meaning of various equivalence principles and the structure of electrodynamics, we give a fairly detailed account of the construction of the light cone and a core metric from the equivalence principle for photons (no birefringence, no polarization rotation and no amplification/attenuation in propagation) in the framework of linear electrodynamics using cosmic connections/observations as empirical support. The cosmic nonbirefringent propagation of photons independent of energy and polarization verifies the Galileo Equivalence Principle (Universality of Propagation) for photons/electromagnetic wave packets in spacetime. This nonbirefringence constrains the spacetime constitutive tensor to high precision to a core metric form with an axion degree and a dilaton degree of freedom. Thus comes the metric with axion and dilation. Constraints on axion and dilaton from astrophysical/cosmic propagation are reviewed. Eötvös-type experiments, Hughes–Drever-type experiments, redshift experiments then constrain and tie this core metric to agree with the matter metric, and hence a unique physical metric and universality of metrology. We summarize these experiments and review how the Galileo equivalence principle constrains the Einstein Equivalence Principle (EEP) theoretically. In local physics this physical metric gives the Lorentz/Poincaré covariance. Understanding that the metric and EEP come from the vacuum as a medium of electrodynamics in the linear regime, efforts to actively look for potential effects beyond this linear scheme are warranted. We emphasize the importance of doing Eötvös-type experiments or other type experiments using polarized bodies/polarized particles. We review the theoretical progress on the issue of gyrogravitational ratio for fundamental particles and update the experimental progress on the measurements of possible long range/intermediate range spin–spin, spin–monopole and spin–cosmos interactions.
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VACARU, SERGIU I. "HORIZONS AND GEODESICS OF BLACK ELLIPSOIDS." International Journal of Modern Physics D 12, no. 03 (March 2003): 479–94. http://dx.doi.org/10.1142/s021827180300272x.
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We analyze the horizon and geodesic structure of a class of 4D off–diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyzed with respect to the adapted frames. We prove that for small deformations (small eccentricities) there are such metrics that the geodesic behaviour is similar to the Schwarzcshild one. We conclude that some vacuum static and stationary ellipsoid configurations1,2 may describe black ellipsoid objects.
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Davis, Marc. "Cosmic structure." International Journal of Modern Physics D 23, no. 10 (September 2014): 1430021. http://dx.doi.org/10.1142/s0218271814300213.
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The history of cosmic structure goes back to the time of Einstein's youth, although few scientists actually thought of the problem of galaxy and cluster formation. The data and ideas were collected slowly as astronomers slowly realized the nature of the problem of large-scale structure. This paper will review several of the key episodes in the history of the field. Starting with the discovery of dark matter in the 30s, the CMBR discovery in the 1960s to the idea of an early episode of inflation in the 1980s, the field has had an acceleration of discovery. In the 80s it was realized that the initial conditions of the universe were specified by the cold dark matter (CDM). Now initial conditions for the formation of structure could be specified for any type of dark matter. With the advent of computing resources, highly nonlinear phases of galaxy formation could be simulated and scientists could ask whether cold dark matter was the correct theory, even on the scale of dwarf spheroidal galaxies, or do the properties of the dwarfs require a different type of dark matter? In an idiosyncratic list, we review several of the key events of the history of cosmic structure, including the first measurements of ξ(r), then the remarkable success of Λ CDM explanations of the large-scale universe. We next turn to velocity fields, the large-scale flow problem, a field which was so promising 20 years ago, and to the baryon acoustic oscillations, a field of remarkable promise today. We review the problem of dwarf galaxies and Lyman-α absorption systems, asking whether the evidence is pointing toward a major switch in our understanding of the nature of dark matter. Finally, we discuss flux anomalies in multiply-lensed systems, which set constraints on the number of dwarf galaxies associated with the lensing galaxy, a topic that is now very interesting since simulations have indicated there should be hundreds of dwarfs orbiting the Milky Way, rather than the 10 that are known. It is quite remarkable that many of the today's results are dependent on techniques first used by Einstein.
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ROJAS, EFRAIN. "HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES." International Journal of Modern Physics D 20, no. 01 (January 2011): 59–75. http://dx.doi.org/10.1142/s0218271811018615.
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The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.
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Cagardová, Denisa, Martin Michalík, Peter Poliak, and Vladimír Lukeš. "Quantum chemical study of electron structure and charge transport properties of symmetric acenequinones." Acta Chimica Slovaca 11, no. 2 (October 1, 2018): 83–93. http://dx.doi.org/10.2478/acs-2018-0013.
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Abstract A systematic theoretical study using density functional theory is presented to estimate the structural, electronic, and charge-transfer characteristics of a symmetric fluorination of acenequinones outer rings. The change in aromaticity of model derivatives was described by different types of aromaticity indices. By considering a hopping mechanism and using the Marcus theory in combination with the Einstein-Smoluchowski relation, electronic drift mobilities were predicted for selected dimer configurations obtained from X-ray structures of anthraquinone, 6,13-pentacenequinone and its octafluorinated derivatives. The analysis of obtained data showed that the fluorination of the outer rings of acenequinones can lower the energy of the lowest unoccupied molecular orbital to the range from −3.0 to −4.0 eV, i.e. typical for organic n-type semiconducting materials. Finally, potential electric semiconductivity of available X-ray structures relating to drift mobilities was discussed.
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REULA, OSCAR, and OLIVIER SARBACH. "A MODEL PROBLEM FOR THE INITIAL-BOUNDARY VALUE FORMULATION OF EINSTEIN'S FIELD EQUATIONS." Journal of Hyperbolic Differential Equations 02, no. 02 (June 2005): 397–435. http://dx.doi.org/10.1142/s0219891605000488.
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In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In particular, they should be compatible with the constraints, yield a well posed initial-boundary value formulation and incorporate some physically desirable properties like, for instance, minimizing reflections of gravitational radiation. Motivated by the problem in General Relativity, we analyze a model problem, consisting of a formulation of Maxwell's equations on a spatially compact region of space–time with timelike boundaries. The form in which the equations are written is such that their structure is very similar to the Einstein–Christoffel symmetric hyperbolic formulations of Einstein's field equations. For this model problem, we specify a family of Sommerfeld-type constraint-preserving boundary conditions and show that the resulting initial-boundary value formulations are well posed. We expect that these results can be generalized to the Einstein–Christoffel formulations of General Relativity, at least in the case of linearizations about a stationary background.
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BURINSKII, ALEXANDER. "THE KERR THEOREM AND MULTI-PARTICLE KERR–SCHILD SOLUTIONS." International Journal of Geometric Methods in Modern Physics 04, no. 03 (May 2007): 437–56. http://dx.doi.org/10.1142/s0219887807002089.
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We discuss an extended version of the Kerr theorem which allows one to construct the exact solutions of the Einstein–Maxwell field equations from a holomorphic generating function F of twistor variables. The exact multi-particle Kerr–Schild solutions are obtained from generating function of the form [Formula: see text], where Fi are partial generating functions for the spinning particles i = 1 ⋯ k. Solutions have an unusual multi-sheeted structure. Twistorial structures of the ith and jth particles do not feel each other, forming a type of its internal space. Gravitational and electromagnetic interaction of the particles occurs via the light-like singular twistor lines. As a result, each particle turns out to be "dressed" by singular pp-strings connecting it to other particles. We argue that this solution may have a relation to quantum theory.
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HERNÁNDEZ, EVA, and ALFREDO MACÍAS. "INDUCED MASSES AND SPIN SELF-INTERACTION FROM FIVE-DIMENSIONAL EINSTEIN–CARTAN–DIRAC THEORY." International Journal of Modern Physics A 13, no. 01 (January 10, 1998): 169–82. http://dx.doi.org/10.1142/s0217751x98000056.
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The Einstein–Cartan theory with a dilaton field coupling arising from five-dimensional principal fiber bundle structure of the metric is investigated. A Dirac type spinor field is coupled to the metric and to translational gauge fields. After the dimensional reduction, the theory introduces a gravitational spin–spin contact interaction coming from the translational degrees of freedom, which is repulsive between Dirac particles whose spins are aligned and attractive when spins are opposed. A classically stable ground state for the dilaton field exists, which is infinitely degenerate with respect to a rescaling of the metric. The induced mass term in the Dirac equation can be interpreted, e.g. as the bare electron mass, as long as we regard this theory as an effective "medium" energy model coming from finite string field theories.
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Min, Fanfei, Chenliang Peng, and Shaoxian Song. "Hydration Layers on Clay Mineral Surfaces in Aqueous Solutions: a Review/Warstwy Uwodnione Na Powierzchni Minerałów Ilastych W Roztworach Wodnych: Przegląd." Archives of Mining Sciences 59, no. 2 (June 1, 2014): 489–500. http://dx.doi.org/10.2478/amsc-2014-0035.
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Abstract Hydration layer on clay mineral surfaces is originated from the adsorption of polar water molecules and hydrated cations on the surfaces through unsaturated ionic bonds, hydrogen bonds and van der Waals bonds. It has attracted great attentions because of their important influences on the dispersive stability of the particles in aqueous solutions. This review highlighted the molecular structure of clay minerals, the origin of hydration layers on clay mineral surfaces, the hydration layer structural model, hydration force and the main parameters of affecting the hydration layers on clay minerals (crystal structure, cationic type and strength, and solution pH). Also, the research methods for hydration layers were briefly described, especially the determination of hydration layer thickness by the Einstein viscosity method and AFM method. In addition, the applications of the stability of fine clay mineral particles in aqueous suspensions were summarized.
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Gover, A. Rod, and Andrew Waldron. "Renormalized volumes with boundary." Communications in Contemporary Mathematics 21, no. 02 (February 27, 2019): 1850030. http://dx.doi.org/10.1142/s021919971850030x.
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We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. These results apply to a wide range of structures. We detail applications in the setting of measures derived from a conformally singular metric. In particular, we show that the anomaly generates invariant ([Formula: see text]-curvature, transgression)-type pairs for hypersurfaces with boundary. For the special case of anomalies coming from the volume enclosed by a minimal hypersurface ending on the boundary of a Poincaré–Einstein structure, this result recovers Branson’s [Formula: see text]-curvature and corresponding transgression. When the singular metric solves a boundary version of the constant scalar curvature Yamabe problem, the anomaly gives generalized Willmore energy functionals for hypersurfaces with boundary. Our approach yields computational algorithms for all the above quantities, and we give explicit results for surfaces embedded in 3-manifolds.
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Khatsymovsky, V. M. "On the discrete version of the Kerr geometry." International Journal of Modern Physics A 36, no. 20 (July 7, 2021): 2150130. http://dx.doi.org/10.1142/s0217751x2150130x.
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In this paper, a Kerr-type solution in the Regge calculus is considered. It is assumed that the discrete general relativity, the Regge calculus, is quantized within the path integral approach. The only consequence of this approach used here is the existence of a length scale at which edge lengths are loosely fixed, as considered in our earlier paper. In addition, we previously considered the Regge action on a simplicial manifold on which the vertices are coordinatized and the corresponding piecewise constant metric is introduced, and found that for the simplest periodic simplicial structure and in the leading order over metric variations between four-simplices, this reduces to a finite-difference form of the Hilbert–Einstein action. The problem of solving the corresponding discrete Einstein equations (classical) with a length scale (having a quantum nature) arises as the problem of determining the optimal background metric for the perturbative expansion generated by the functional integral. Using a one-complex-function ansatz for the metric, which reduces to the Kerr–Schild metric in the continuum, we find a discrete metric that approximates the continuum one at large distances and is nonsingular on the (earlier) singularity ring. The effective curvature [Formula: see text], including where [Formula: see text] (gravity sources), is analyzed with a focus on the vicinity of the singularity ring.
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Serrano-Sánchez, Federico, Norbert M. Nemes, José Luis Martínez, Oscar Juan-Dura, Marco Antonio de la Torre, Maria Teresa Fernández-Díaz, and José Antonio Alonso. "Structural evolution of a Ge-substituted SnSe thermoelectric material with low thermal conductivity." Journal of Applied Crystallography 51, no. 2 (February 6, 2018): 337–43. http://dx.doi.org/10.1107/s1600576718000808.
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Thermoelectric materials are expected to become new alternative sources of sustainable energy. Among them, the SnSe intermetallic alloy has been described as an excellent thermoelectric compound, characterized by an extremely low thermal conductivity with maximum performance at the onset of a structural phase transition at 800 K. Recently, novel SnSe derivatives with Ge substitution have been synthesized by a direct arc-melting technique. This produces nanostructured polycrystalline samples that exhibit a record high Seebeck coefficient, anticipating an excellent performance above room temperature. Here, the structural phase transition from a GeS-type structure (space groupPnma) to a TlI-type structure (space groupCmcm) is investigatedin situ vianeutron powder diffraction (NPD) in the temperature range 298–853 K for the selected composition Sn0.8Ge0.2Se. This transition takes place at 803 K, as shown by differential scanning calorimetry. The analysis from the NPD data shows a non-monotonic behaviour of the anisotropic displacement parameters upon entering the domain of theCmcmstructure. The energies of the atomic vibrations have been quantitatively analysed by fitting the temperature-dependent mean-square displacements to Einstein oscillators. The thermal conductivity of Sn0.8Ge0.2Se is as low as 0.35 W m−1 K−1at 773 K, which mostly represents the lattice thermal contribution.
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Gladush, V. D. "SPHERICALLY SYMMETRIC SYSTEM OF GRAVITATIONAL AND ELECTROMAGNETIC FIELDS AND THE STRUCTURE OF ITS CONFIGURATION SPACE." Odessa Astronomical Publications 35 (December 14, 2022): 4–9. http://dx.doi.org/10.18524/1810-4215.2022.35.268190.
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Geometrodynamics of charged black holes (BH) described by the system of Maxwell Einstein equations is considered. We start from a spherically symmetric metric, a reduced action, and a Lagrangian written in characteristic variables. The configuration space (CS) metric, Hamiltonian, momentum and electromagnetic constraints are constructed. The system has conservation laws of charge q and mass m. The action functional is transformed into a Jacobi-type functional in CS with a metric conformal to the CS metric. A transformation of field variables is introduced which brings the CS metric to the "Lorentzian"form. The resulting CS metric is the metric of a flat nonholonomic section of a 4-dimensional space. In the new variables, the squared momenta of the system has the Lorentz form. On this basis, quantization is considered. Thanks to the structure of the CS, the momentum operators, the DeWitt equations, and the mass and charge operators are constructed. The equations system of CBH quantum states with certain q and m is constructed. For comparison, we consider the CBH reduced model limited in the T-region. In such the simplified formulation, the T-model equations are integrated and lead to the CBH with continuous spectrum of m and q.
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Otoniel, Edson, R. V. Lobato, M. Malheiro, Bruno Franzon, Stefan Schramm, and Fridolin Weber. "White Dwarf Pulsars and Very Massive Compact Ultra Magnetized White Dwarfs." International Journal of Modern Physics: Conference Series 45 (January 2017): 1760024. http://dx.doi.org/10.1142/s2010194517600242.
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In this work, we discuss white dwarf pulsars found recently making also reference of the possibility of some SGRs/AXPs being part of this class of pulsars. We also study the properties of very massive compact ultra magnetized white dwarfs that could be the progenitors candidates of super luminous type Ia supernovae, and also a previous stage of these white dwarf pulsars before the magnetic field decay.The structure of this ultra magnetized white dwarfs is obtained by solving the Einstein-Maxwell equations with a poloidal magnetic field in a fully general relativistic approach. The stellar interior is composed of a regular crystal lattice made of carbon ions immersed in a degenerate relativistic electron gas. We find that magnetized white dwarfs violate the standard Chandrasekhar mass limit significantly. We obtain a maximum white dwarf mass of around [Formula: see text] with an equatorial radius [Formula: see text] Km, a central magnetic field of [Formula: see text] G and [Formula: see text] G at the stellar surface.
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MENEZES, J., C. SANTOS, and P. P. AVELINO. "GRAVITATIONAL EFFECTS OF VARYING ALPHA STRINGS." International Journal of Modern Physics A 21, no. 16 (June 30, 2006): 3295–306. http://dx.doi.org/10.1142/s0217751x06031430.
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We study spatial variations of the fine-structure constant in the presence of static straight cosmic strings in the weak-field approximation in Einstein gravity. We work in the context of a generic Bekenstein-type model and consider a gauge kinetic function linear in the scalar field. We determine an analytical form for the scalar field and the string metric at large distances from the core. We show that the gravitational effects of α-varying strings can be seen as a combination of the gravitational effects of global and local strings. We also verify that at large distances to the core the space–time metric is similar to that of a global string. We study the motion of test particles approaching from infinity and show that photons are scattered to infinity while massive particles are trapped in bounded trajectories. We also calculate an overall limit on the magnitude of the variation of α for a GUT string, by considering suitable cosmological constraints coming from the Equivalence Principle.
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Mathew, Titus K., Chinthak Murali, and J. Shejeelammal. "Evolution of non-interacting entropic dark energy and its phantom nature." Modern Physics Letters A 31, no. 12 (April 19, 2016): 1650071. http://dx.doi.org/10.1142/s0217732316500711.
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Assuming the form of the entropic dark energy (EDE) as it arises from the surface term in the Einstein–Hilbert’s action, its evolution was analyzed in an expanding flat universe. The model parameters were evaluated by constraining the model using the Union data on Type Ia supernovae. We found that in the non-interacting case, the model predicts an early decelerated phase and a later accelerated phase at the background level. The evolutions of the Hubble parameter, dark energy (DE) density, equation of state parameter and deceleration parameter were obtained. The model hardly seems to be supporting the linear perturbation growth for the structure formation. We also found that the EDE shows phantom nature for redshifts z [Formula: see text] 0.257. During the phantom epoch, the model predicts big rip effect at which both the scale factor of expansion and the DE density become infinitely large and the big rip time is found to be around 36 Giga years from now.
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Dey, Kajal Krishna, and Golam Ali Sekh. "Coupled matter-wave solitons on oscillating reflectors under the effects of gravity." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 8 (August 2022): 083149. http://dx.doi.org/10.1063/5.0096721.
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We consider coupled matter-waves solitons in Bose–Einstein condensates and study the dynamics under the combined effects of gravity and reflecting potential. The dynamics of matter-wave near a reflector oscillating periodically with time generates the dynamics of a special kind of localized structure called oscillon. We derive a mechanical model for the coupled oscillon dynamics. We pay special attention to the inter-component interaction and see that effective potential depends on the type (repulsive/attractive) and strength of interaction. We find that the inter-component interaction affects the frequency of oscillation and introduces an initial phase-shift between the reflector and the oscillon. This phase-shift, in addition to instantaneous phase change due to the oscillation of the reflector, results in interesting dynamics. The coupled oscillon is found to execute quasi-periodic and chaotic dynamics for both attractive and repulsive inter-component interactions. We analyze the maximum value of Lyapunov exponents and show that the dynamical response of the coupled oscillon depends on the ratio of the center of mass position and their separation.
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Bocharov, Dmitry, Inga Pudza, Konstantin Klementiev, Matthias Krack, and Alexei Kuzmin. "Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy." Materials 14, no. 18 (September 10, 2021): 5206. http://dx.doi.org/10.3390/ma14185206.
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Wurtzite-type zinc oxide (w-ZnO) is a widely used material with a pronounced structural anisotropy along the c axis, which affects its lattice dynamics and represents a difficulty for its accurate description using classical models of interatomic interactions. In this study, ab initio molecular dynamics (AIMD) was employed to simulate a bulk w-ZnO phase in the NpT ensemble in the high-temperature range from 300 K to 1200 K. The results of the simulations were validated by comparison with the experimental Zn K-edge extended X-ray absorption fine structure (EXAFS) spectra and known diffraction data. AIMD NpT simulations reproduced well the thermal expansion of the lattice, and the pronounced anharmonicity of Zn–O bonding was observed above 600 K. The values of mean-square relative displacements and mean-square displacements for Zn–O and Zn–Zn atom pairs were obtained as a function of interatomic distance and temperature. They were used to calculate the characteristic Einstein temperatures. The temperature dependences of the O–Zn–O and Zn–O–Zn bond angle distributions were also determined.
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CHO, Y. M., D. G. PAK, and B. S. PARK. "A MINIMAL MODEL OF LORENTZ GAUGE GRAVITY WITH DYNAMICAL TORSION." International Journal of Modern Physics A 25, no. 14 (June 10, 2010): 2867–82. http://dx.doi.org/10.1142/s0217751x10048524.
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A new Lorentz gauge gravity model with R2-type Lagrangian is proposed. In the absence of classical torsion, the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space–time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin-2 mode of torsion becomes dynamical essentially due to the nonlinear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space–time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion.
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Wu, Yue-Liang. "Theory of quantum gravity beyond Einstein and space-time dynamics with quantum inflation." International Journal of Modern Physics A 30, no. 28n29 (October 20, 2015): 1545002. http://dx.doi.org/10.1142/s0217751x15450025.
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In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A bi-frame space-time is initiated to describe the laws of nature. One frame space-time is a globally flat coordinate Minkowski space-time that acts as an inertial reference frame for the motions of fields, the other is a locally flat non-coordinate Gravifield space-time that functions as an interaction representation frame for the degrees of freedom of fields. The Gravifield is sided on both the globally flat coordinate space-time and locally flat non-coordinate space-time and characterizes the gravitational force. Instead of the principle of general coordinate invariance in Einstein theory of general relativity, some underlying principles with the postulates of coordinate independence and gauge invariance are motivated to establish the theory of quantum gravity. When transmuting the Gravifield basis into the coordinate basis in Minkowski space-time, it enables us to obtain equations of motion for all quantum fields and derive basic conservation laws for all symmetries. The gravity equation is found to be governed by the total energy–momentum tensor defined in the flat Minkowski space-time. When the spinnic and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we arrive at a Lorentz invariant and conformally flat background Gravifield space-time that is characterized by a cosmic vector with a non-zero cosmological mass scale. We also obtain the massless graviton and massive spinnon. The resulting universe is in general not isotropic in terms of conformal proper time and turns out to be inflationary in light of cosmic proper time. The conformal size of the universe has a singular at the cosmological horizon to which the cosmic proper time must be infinitely large. We show a mechanism for quantum inflation caused by the quantum loop contributions. The Gravifield behaves as a Goldstone-like field that transmutes the local spinnic gauge symmetry into the global Lorentz symmetry, which makes the spinnic gauge field becomes a hidden gauge field. As a consequence, the bosonic gravitational interactions can be described by the Goldstone-like Gravimetric field and space-time gauge field. The Einstein theory of general relativity is expected to be an effective low energy theory. Two types of gravity equation are resulted, one is the extension to Einstein’s equation of general relativity, and the other is a new type of gravitational equation that characterizes the spinnon dynamics.
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Su, Chuan-Qi, Yi-Tian Gao, Qi-Min Wang, Jin-Wei Yang, and Da-Wei Zuo. "Nonautonomous solitons in terms of the double Wronskian determinant for a variable-coefficient Gross–Pitaevskii equation in the Bose–Einstein condensate." Modern Physics Letters B 30, no. 09 (April 10, 2016): 1650103. http://dx.doi.org/10.1142/s0217984916501037.
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Under investigation in this paper is a variable-coefficient Gross–Pitaevskii equation which describes the Bose–Einstein condensate. Lax pair, bilinear forms and bilinear Bäcklund transformation for the equation under some integrable conditions are derived. Based on the Lax pair and bilinear forms, double Wronskian solutions are constructed and verified. The [Formula: see text]th-order nonautonomous solitons in terms of the double Wronskian determinant are given. Propagation and interaction for the first- and second-order nonautonomous solitons are discussed from three cases. Amplitudes of the first- and second-order nonautonomous solitons are affected by a real parameter related to the variable coefficients, but independent of the gain-or-loss coefficient [Formula: see text] and linear external potential coefficient [Formula: see text]. For Case 1 [Formula: see text], [Formula: see text] leads to the accelerated propagation of nonautonomous solitons. Parabolic-, cubic-, exponential- and cosine-type nonautonomous solitons are exhibited due to the different choices of [Formula: see text]. For Case 2 [Formula: see text], if the real part of the spectral parameter equals 0, stationary soliton can be formed. If we take the harmonic external potential coefficient [Formula: see text] as a positive constant and let the real parts of the two spectral parameters be the same, bound-state-like structures can be formed, but there are only one attractive and two repulsive procedures. For Case 3 [[Formula: see text] and [Formula: see text] are taken as nonzero constants], head-on interaction, overtaking interaction and bound-state structure can be formed based on the signs of the two spectral parameters.
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Grillo, C. "Luminous and dark matter in early-type lens galaxies." Proceedings of the International Astronomical Union 5, H15 (November 2009): 70. http://dx.doi.org/10.1017/s1743921310008252.
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In the past few years gravitational lensing has allowed astrophysicists to make great progress in the understanding of the internal structure of early-type galaxies. By taking advantage of accurate photometric and spectroscopic measurements, the luminous and dark matter content of lens galaxies can in principle be disentangled (e.g., Grillo et al. 2008, 2009). SDSS J1538+5817 is an extraordinary strong lensing system composed of an elliptical galaxy and two equally-distant sources located, respectively, at redshifts 0.143 and 0.531 (Grillo et al., submitted to ApJ). The sources are lensed into two and four images with an almost complete Einstein ring, covering a rather large region on the lens plane. By using HST/ACS and WFPC2 imaging and NOT/ALFOSC spectroscopy, we have investigated the lens total mass distribution within one effective radius. Then, we have fitted the SDSS multicolor photometry of the galaxy with composite stellar population models to obtain its luminous mass. By combining lensing and photometric measurements, we have estimated the lens mass in terms of luminous and dark matter components and studied the global properties of the dark matter halo. The exceptional lensing configuration of this system has allowed us to conclude that the galaxy dark matter density distribution is shallower and more diffused than the luminous one and the former starts exceeding the latter at a distance of approximately 1.5 times the effective radius. Extending these results to a larger number of lenses would help us to decipher the processes that rule galaxy formation and evolution in the LCDM scenario.
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Treu, Tommaso, Léon V. E. Koopmans, David J. Sand, Graham P. Smith, and Richard S. Ellis. "The dark matter halos of spheroidal galaxies and clusters of galaxies." Symposium - International Astronomical Union 220 (2004): 159–64. http://dx.doi.org/10.1017/s0074180900183093.
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We describe the first results from two observational projects aimed at measuring the amount and spatial distribution of dark matter in distant early-type galaxies (E/S0s) and clusters of galaxies. At the galaxy scale, the Lenses Structure and Dynamics (LSD) Survey is gathering kinematic data for distant (up to z ⋐ 1) E/S0s that are gravitational lenses. A joint lensing and dynamical analysis constrains the fraction of dark matter within the Einstein radius, the mass-to-light ratio of the stellar component, and the total slope of the mass density profile. These properties and their evolution with redshift are briefly discussed in terms of the formation and evolution of E/S0 galaxies and measurement of the Hubble Constant from gravitational time delay systems. At the cluster scale – after careful removal of the stellar component with a joint lensing and dynamical analysis – systems with giant radial arcs can be used to measure precisely the inner slope of the dark matter halo. An HST search for radial arcs and the analysis of a first sample are briefly discussed in terms of the universal dark matter halos predicted by CDM simulations.
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ANCO, STEPHEN C. "GAUGE THEORY DEFORMATIONS AND NOVEL YANG–MILLS CHERN–SIMONS FIELD THEORIES WITH TORSION." International Journal of Geometric Methods in Modern Physics 01, no. 04 (August 2004): 493–544. http://dx.doi.org/10.1142/s0219887804000265.
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A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The physical interest in studying deformations is to address uniqueness of known nonlinear interactions of gauge fields and to look systematically for theoretical possibilities for new interactions. Mathematically, the study of deformations aims to understand the rigidity of the nonlinear structure of gauge field theories and to uncover new types of nonlinear geometrical structures. The first part of this paper summarizes and significantly elaborates a field-theoretic deformation method developed in earlier work. Some key contributions presented here are, firstly, that the determining equations for deformation terms are shown to have an elegant formulation using Lie derivatives in the jet space associated with the gauge field variables. Secondly, the obstructions (integrability conditions) that must be satisfied by lowest-order deformations terms for existence of a deformation to higher orders are explicitly identified. Most importantly, a universal geometrical structure common to a large class of nonlinear gauge theory examples is uncovered. This structure is derived geometrically from the deformed gauge symmetry and is characterized by a covariant derivative operator plus a nonlinear field strength, related through the curvature of the covariant derivative. The scope of these results encompasses Yang–Mills theory, Freedman–Townsend theory, and Einstein gravity theory, in addition to their many interesting types of novel generalizations that have been found in the past several years. The second part of the paper presents a new geometrical type of Yang–Mills generalization in three dimensions motivated from considering torsion in the context of nonlinear sigma models with Lie group targets (chiral theories). The generalization is derived by a deformation analysis of linear abelian Yang–Mills Chern–Simons gauge theory. Torsion is introduced geometrically through a duality with chiral models obtained from the chiral field form of self-dual (2+2) dimensional Yang–Mills theory under reduction to (2+1) dimensions. Field-theoretic and geometric features of the resulting nonlinear gauge theories with torsion are discussed.
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Булавин, Viktor Ivanovych, Ivan Nikolajevych V’unik, Andrii Viktorovych Kramarenko, and Alexandr Ivanovych Rusinov. "NEAR HYDRATION OF SINGLY CHARGED MONOATOMIC IONS IN EXTREMELY DILUTED SOLUTIONS: THE EFFECT OF TEMPERATURE AND PRESSURE." Bulletin of the National Technical University "KhPI". Series: Chemistry, Chemical Technology and Ecology, no. 1(5) (May 15, 2021): 24–31. http://dx.doi.org/10.20998/2079-0821.2021.01.04.
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The diffusion coefficient and the distance of translational displacement of Li+, Na+ K+, Cs+, Cl– and Br– ions in water at 298.15 K – 423.15 K (25 K step) and pressure from 0.0981 to 784.5 MPa (98.1 MPa step) were calculated from the literature data on limiting molar electrical conductivity. The values for these ions increase with pressure growth from 0.0981 to 98.1 MPa at 298.15 K. Further pressure increase (up to 785 MPa) leads to decrease in . Temperature growth under isobaric conditions leads to an increase in . Parameter (– ri) (deviation from the Stokes–Einstein law, ri is ion structural radius) was used as a criterion for the type of ion solvation. It is shown that Li+ and Na+ ions behave as cosmotropes, or positively solvated structure–forming ions having (– ri) > 0. The Cs+, Cl–, Br– ions behave as chaotropes, or negatively solvated structure–breaking ions having (– ri) < 0. For the K+ ion, the (– ri) deviation is alternating. At 0.0981 MPa and 298.15 K, the K+ ion is a chaotrope. But at 320 K (Tlim) parameter (– ri) = 0. It corresponds to the transition from negative to positive solvation. Above Tlim at P = const, the K+ ion is a cosmotrope. At 298.15 K and up to 98.1 MPa, the pressure causes the same change in the (– ri) deviation as the temperature. On the contrary, at 320 K and higher, the pressure affects the near hydration in the direction opposite to the temperature.
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Cremaschini, Claudio, and Massimo Tessarotto. "Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity." Entropy 23, no. 5 (April 23, 2021): 511. http://dx.doi.org/10.3390/e23050511.
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A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width δr between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.
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Keel, William C., Jean Tate, O. Ivy Wong, Julie K. Banfield, Chris J. Lintott, Karen L. Masters, Brooke D. Simmons, et al. "Gems of the Galaxy Zoos—A Wide-ranging Hubble Space Telescope Gap-filler Program*." Astronomical Journal 163, no. 4 (March 7, 2022): 150. http://dx.doi.org/10.3847/1538-3881/ac517d.
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Abstract We describe the Gems of the Galaxy Zoos (Zoo Gems) project, a gap-filler project using short windows in the Hubble Space Telescope's schedule. As with previous snapshot programs, targets are taken from a pool based on position; we combine objects selected by volunteers in both the Galaxy Zoo and Radio Galaxy Zoo citizen-science projects. Zoo Gems uses exposures with the Advanced Camera for Surveys to address a broad range of topics in galaxy morphology, interstellar-medium content, host galaxies of active galactic nuclei, and galaxy evolution. Science cases include studying galaxy interactions, backlit dust in galaxies, post-starburst systems, rings and peculiar spiral patterns, outliers from the usual color–morphology relation, Green Pea compact starburst systems, double radio sources with spiral host galaxies, and extended emission-line regions around active galactic nuclei. For many of these science categories, final selection of targets from a larger list used public input via a voting process. Highlights to date include the prevalence of tightly wound spiral structure in blue, apparently early-type galaxies, a nearly complete Einstein ring from a group lens, redder components at lower surface brightness surrounding compact Green Pea starbursts, and high-probability examples of spiral galaxies hosting large double radio sources.
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TARTAGLIA, ANGELO. "A STRAINED SPACE-TIME TO EXPLAIN THE LARGE SCALE PROPERTIES OF THE UNIVERSE." International Journal of Modern Physics: Conference Series 03 (January 2011): 303–11. http://dx.doi.org/10.1142/s2010194511001401.
Full textAbstract:
Space-time can be treated as a four-dimensional material continuum. The corresponding generally curved manifold can be thought of as having been obtained, by continuous deformation, from a flat four-dimensional Euclidean manifold. In a three-dimensional ordinary situation such a deformation process would lead to strain in the manifold. Strain in turn may be read as half the difference between the actual metric tensor and the Euclidean metric tensor of the initial unstrained manifold. On the other side we know that an ordinary material would react to the attempt to introduce strain giving rise to internal stresses and one would have correspondingly a deformation energy term. Assuming the conditions of linear elasticity hold, the deformation energy is easily written in terms of the strain tensor. The Einstein-Hilbert action is generalized to include the new deformation energy term. The new action for space-time has been applied to a Friedmann-Lemaître-Robertson-Walker universe filled with dust and radiation. The accelerated expansion is recovered, then the theory has been put through four cosmological tests: primordial isotopic abundances from Big Bang Nucleosynthesis; Acoustic Scale of the CMB; Large Scale Structure formation; luminosity/redshift relation for type Ia supernovae. The result is satisfying and has allowed to evaluate the parameters of the theory.