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1
Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 9, no. 3 (2012): 2269–333. http://dx.doi.org/10.4171/owr/2012/37.
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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 12, no. 3 (2015): 1867–935. http://dx.doi.org/10.4171/owr/2015/33.
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Cederbaum, Carla, Mihalis Dafermos, James A. Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 18, no. 3 (November 25, 2022): 2157–267. http://dx.doi.org/10.4171/owr/2021/40.
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Seidel, Edward, and Wai-Mo Suen. "NUMERICAL RELATIVITY." International Journal of Modern Physics C 05, no. 02 (April 1994): 181–87. http://dx.doi.org/10.1142/s012918319400012x.
Повний текст джерелаАнотація:
The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques. A set of tools is developed for determining gauge choices, setting boundary and initial conditions, handling spacetime singularities, etc. As required by the special physical and mathematical properties of general relativity, such techniques are indispensable for the numerical evolutions of spacetime. (3) Coding. The optimal use of parallel processing is crucial for many problems in numerical relativity, due to the intrinsic complexity of the theory. (4) Visualization. Numerical relativity is about the evolutions of 3-dimensional geometric structures. There are special demands on visualization. (5) Interpretation and Understanding. The integration of numerical data in relativity into a consistent physical picture is complicated by gauge and coordinate degrees of freedoms and other difficulties. We give a brief overview of the progress made in these areas.
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Benedetto, Elmo, and Fabiano Feleppa. "Underlining some mathematical and physical aspects about the concept of motion in general relativity." Afrika Matematika 29, no. 3-4 (January 24, 2018): 349–56. http://dx.doi.org/10.1007/s13370-018-0545-9.
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Kolhe, K. G. "Relativity of Pseudo-Spherical Concept and Hartree-Fock Concept for Condensed Matter." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (August 31, 2022): 1839–41. http://dx.doi.org/10.22214/ijraset.2022.46529.
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Abstract: The function Fn,l (r) ;the radial part of of the pseudo-wave function k (r, , ) is expressed in terms of ion-core electron density, n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and helpful in determining many types of electron densities. The physical and mathematical developments on various aspects such as functional densities have been described. It is further emphasized that Fn,l (r) and Pn,l (r) functions and core electron density at different electronic states of the atom that both the functions posses strong correlationship. Study concludes that the present development resulted into an innovative simpler path in the orientation of condensed matter as well as Mathematical Physics.
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GAMBINI, RODOLFO, and JORGE PULLIN. "CLASSICAL AND QUANTUM GENERAL RELATIVITY: A NEW PARADIGM." International Journal of Modern Physics D 14, no. 12 (December 2005): 2355–60. http://dx.doi.org/10.1142/s0218271805007917.
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We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.
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Lin, De-Hone. "The 2+1-Dimensional Special Relativity." Symmetry 14, no. 11 (November 14, 2022): 2403. http://dx.doi.org/10.3390/sym14112403.
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In the new mathematical description of special relativity in terms of the relativistic velocity space, many physical aspects acquire new geometric meanings. Performing conformal deformations upon the 2-dimensional relativistic velocity space for the (2+1)-dimensional special relativity, we find that these conformal deformations correspond to the generalized Lorentz transformations, which are akin to the ordinary Lorentz transformation, but are morphed by a global rescaling of the polar angle and correspondingly characterized by a topological integral index. The generalized Lorentz transformations keep the two fundamental principles of special relativity intact, suggesting that the indexed generalization may be related to the Bondi–Metzner–Sachs (BMS) group of the asymptotic symmetries of the spacetime metric. Furthermore, we investigate the Doppler effect of light, the Planck photon rocket, and the Thomas precession, affirming that they all remain in the same forms of the standard special relativity under the generalized Lorentz transformation. Additionally, we obtain the general formula of the Thomas precession, which gives a clear geometric meaning from the perspective of the gauge field theory in the relativistic velocity space.
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Nandi, Kamal K. "Some Aspects of Minimally Relativistic Newtonian Gravity." Zeitschrift für Naturforschung A 46, no. 12 (December 1, 1991): 1026–32. http://dx.doi.org/10.1515/zna-1991-1205.
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Abstract This paper aims to examine if the classical tests of General Relativity (GR) can be predicted by a simpler approach based on minimal changes in the Newtonian gravity. The approach yields a precession of the perihelion of Mercury by an amount 39.4"/century which is very close to the observed Dicke-Goldenberg value (39.6"/century), but less than the popularly accepted value (43"/ century). The other tests exactly coincide with those of GR. Our analysis also displays the genesis as well as the role of geometry in the description of gravitational processes. The time dependent spherically symmetric equations, which are mathematically interesting, call for a further study. The model also allows unambiguous formulation of conservation laws. On the whole, the paper illustrates the limited extent to which a second rank tensor analogy (nonlinear) with flat background Faraday-Maxwell electrodynamics can be pushed in describing gravitation
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MURDZEK, R. "THE GEOMETRY OF THE TORUS UNIVERSE." International Journal of Modern Physics D 16, no. 04 (April 2007): 681–86. http://dx.doi.org/10.1142/s0218271807009826.
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In this contribution, we show that the cyclic universe models naturally emerge from torus geometry in a braneworld scenario. The Riemannian metric on torus and the fundamental tensors of the General Relativity are derived. A discussion on particular aspects of this model is also given.
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De Falco, Vittorio. "New Approaches to the General Relativistic Poynting-Robertson Effect." Emerging Science Journal 4, no. 3 (June 1, 2020): 214–27. http://dx.doi.org/10.28991/esj-2020-01225.
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Objectives: A systematic study on the general relativistic Poynting-Robertson effect has been developed so far by introducing different complementary approaches, which can be mainly divided in two kinds: (1) improving the theoretical assessments and model in its simple aspects, and (2) extracting mathematical and physical information from such system with the aim to extend methods or results to other similar physical systems of analogue structure. Methods/Analysis: We use these theoretical approaches: relativity of observer splitting formalism; Lagrangian formalism and Rayleigh potential with a new integration method; Lyapunov theory os stability. Findings: We determined the three-dimensional formulation of the general relativistic Poynting-Robertson effect model. We determine the analytical form of the Rayleigh potential and discuss its implications. We prove that the critical hypersurfaces (regions where there is a balance between gravitational and radiation forces) are stable configurations. Novelty/Improvement: Our new contributions are: to have introduced the three-dimensional description; to have determined the general relativistic Rayleigh potential for the first time in the General Relativity literature; to have provided an alternative, general and more elegant proof of the stability of the critical hypersurfaces.
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Stuckey, W. Mark, Timothy McDevitt, and Michael Silberstein. ""Mysteries" of Modern Physics and the Fundamental Constants c, h, and G." Quanta 11, no. 1 (June 15, 2022): 5–14. http://dx.doi.org/10.12743/quanta.v11i1.189.
Повний текст джерелаАнотація:
We review how the kinematic structures of special relativity and quantum mechanics both stem from the relativity principle, i.e., "no preferred reference frame" (NPRF). Essentially, NPRF applied to the measurement of the speed of light c gives the light postulate and leads to the geometry of Minkowski space, while NPRF applied to the measurement of Planck's constant h gives "average-only" projection and leads to the denumerable-dimensional Hilbert space of quantum mechanics. These kinematic structures contain the counterintuitive aspects ("mysteries") of time dilation, length contraction, and quantum entanglement. In this essay, we extend the application of NPRF to the gravitational constant G and show that it leads to the "mystery" of the contextuality of mass in general relativity. Thus, we see an underlying coherence and integrity in modern physics via its "mysteries" and the fundamental constants c, h, and G. It is well known that Minkowski and Einstein were greatly influenced by David Hilbert in their development of special relativity and general relativity, respectively, but relating those theories to quantum mechanics via its non-Boolean Hilbert space kinematics is perhaps surprising.Quanta 2022; 11: 5–14.
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Et. al., Dr Indrajit Patra ,. "Shifts in the Foundation: The Continual Modification and Generalization of Axioms and the Search for the Mathematical Principles that Underlie our Reality." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 11, 2021): 1095–106. http://dx.doi.org/10.17762/turcomat.v12i2.1126.
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The study shall seek to explore the deep, underlying correspondence between the mathematical world of pure numbers and our physical reality. The study begins by pointing out that while the familiar, one-dimensional real numbers quantify many aspects of our day-to-day reality, complex numbers provide the mathematical foundations of quantum mechanics and also describe the behavior of more complicated quantum networks and multi-party correlations, and quaternions underlie Einsteinian special theory of relativity, and then poses the question whether the octonions could play a similar role in constructing a grander theory of our universe. The study then points out that by increasing the level of abstraction and generalization of axiomatic assumptions, we could construct a more powerful number system based on octonions, the seditions, or even other hypercomplex numbers so that we may more accurately describe the universe in its totality.
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Song, Shi Gang, Xia Xia Hu, Jian Liu, and Jian Ma. "Research of Machine Tool Reconfiguration Based on Reliability." Applied Mechanics and Materials 184-185 (June 2012): 397–401. http://dx.doi.org/10.4028/www.scientific.net/amm.184-185.397.
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To adapt to agile workshop environment, the reliability of reconfiguration machine tool was analyzed, and the mathematical models of reconfiguration machine tools’ reliability guideline was established. By modular design of reconfiguration machine tool, the general idea of machine tool reconfiguration oriented to reliability was presented. The machine tool reconfiguration method based on modularization was researched mostly in such aspects as relativity analysis, module reconfiguration of lacking ability parameter, module reconfiguration of redundancy ability parameter. The method solved the rapidity reconfiguration ability of machine tool in system reconfiguration, utilized availability resource reasonably.
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Vizgin, Vladimir P. "Albert Einstein’s Epistemic Virtues and Vices." Epistemology & Philosophy of Science 58, no. 4 (2021): 175–95. http://dx.doi.org/10.5840/eps202158468.
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The article is based on the concepts of epistemic virtues and epistemic vices and explores A. Einstein’s contribution to the creation of fundamental physical theories, namely the special theory of relativity and general theory of relativity, as well as to the development of a unified field theory on the basis of the geometric field program, which never led to success. Among the main epistemic virtues that led Einstein to success in the construction of the special theory of relativity are the following: a unique physical intuition based on the method of thought experiment and the need for an experimental justification of space-time concepts; striving for simplicity and elegance of theory; scientific courage, rebelliousness, signifying the readiness to engage in confrontation with scientific conventional dogmas and authorities. In the creation of general theory of relativity, another intellectual virtue was added to these virtues: the belief in the heuristic power of the mathematical aspect of physics. At the same time, he had to overcome his initial underestimation of the H. Minkowski’s four-dimensional concept of space and time, which has manifested in a distinctive flexibility of thinking typical for Einstein in his early years. The creative role of Einstein’s mistakes on the way to general relativity was emphasized. These mistakes were mostly related to the difficulties of harmonizing the mathematical and physical aspects of theory, less so to epistemic vices. The ambivalence of the concept of epistemic virtues, which can be transformed into epistemic vices, is noted. This transformation happened in the second half of Einstein’s life, when he for more than thirty years unsuccessfully tried to build a unified geometric field theory and to find an alternative to quantum mechanics with their probabilistic and Copenhagen interpretation In this case, we can talk about the following epistemic vices: the revaluation of mathematical aspect and underestimation of experimentally – empirical aspect of the theory; adopting the concepts general relativity is based on (continualism, classical causality, geometric nature of fundamental interactions) as fundamental; unprecedented persistence in defending the GFP (geometrical field program), despite its failures, and a certain loss of the flexibility of thinking. A cosmological history that is associated both with the application of GTR (general theory of relativity) to the structure of the Universe, and with the missed possibility of discovering the theory of the expanding Universe is intermediate in relation to Einstein’s epistemic virtues and vices. This opportunity was realized by A.A. Friedmann, who defeated Einstein in the dispute about if the Universe was stationary or nonstationary. In this dispute some of Einstein’s vices were revealed, which Friedman did not have. The connection between epistemic virtues and the methodological principles of physics and also with the “fallibilist” concept of scientific knowledge development has been noted.
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BILLYARD, ANDREW, PAUL S. WESSON, and DIMITRI KALLIGAS. "PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY." International Journal of Modern Physics D 04, no. 05 (October 1995): 639–59. http://dx.doi.org/10.1142/s0218271895000430.
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The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.
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Kouneiher, Joseph, and Cécile Barbachoux. "Cartan's soldered spaces and conservation laws in physics." International Journal of Geometric Methods in Modern Physics 12, no. 09 (October 2015): 1550089. http://dx.doi.org/10.1142/s0219887815500899.
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In this paper, we will introduce a generalized soldering p-forms geometry, which can be the right framework to describe many new approaches and concepts in modern physics. Here we will treat some aspects of the theory of local cohomology in fields theory or more precisely the theory of soldering-form conservation laws in physics. We provide some illustrative applications, primarily taken from the Einstein equations of general theory of relativity and Yang–Mills theory. This theory can be considered to be a generalization of Noether's theory of conserved current to differential forms of any degree. An essential result of this, is that the conservation of the energy–momentum in general relativity, is linked to the fact that the vacuum field equations are equivalent to the integrability conditions of a first-order system of differential equations. We also apply the idea of the soldered space and the integrability conditions to the case of Yang–Mills theory. The mathematical framework, where these intuitive considerations would fit naturally, can be used to describe also the dynamics of changing manifolds.
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Rubiera-Garcia, Diego. "From fundamental physics to tests with compact objects in metric-affine theories of gravity." International Journal of Modern Physics D 29, no. 11 (May 26, 2020): 2041007. http://dx.doi.org/10.1142/s0218271820410072.
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This paper provides a short but comprehensible overview of some relevant aspects of metric-affine theories of gravity in relation to the physics and astrophysics of compact objects. We shall highlight the pertinence of this approach to supersede General Relativity on its strong-field regime, as well as its advantages and some of its difficulties. Moreover, we shall reflect on the present and future opportunities to test its predictions with relativistic and nonrelativistic stars, black holes, and other exotic horizonless compact objects.
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NI, WEI-TOU. "EMPIRICAL FOUNDATIONS OF THE RELATIVISTIC GRAVITY." International Journal of Modern Physics D 14, no. 06 (June 2005): 901–21. http://dx.doi.org/10.1142/s0218271805007139.
Повний текст джерелаАнотація:
In 1859, Le Verrier discovered the mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 141 years to 2000, the precisions of laboratory and space experiments, and astrophysical and cosmological observations on relativistic gravity have been improved by 3 orders of magnitude. In 1999, we envisaged a 3–6 order improvement in the next 30 years in all directions of tests of relativistic gravity. In 2000, the interferometric gravitational wave detectors began their runs to accumulate data. In 2003, the measurement of relativistic Shapiro time-delay of the Cassini spacecraft determined the relativistic-gravity parameter γ to be 1.000021 ± 0.000023 of general relativity — a 1.5-order improvement. In October 2004, Ciufolini and Pavlis reported a measurement of the Lense–Thirring effect on the LAGEOS and LAGEOS2 satellites to be 0.99 ± 0.10 of the value predicted by general relativity. In April 2004, Gravity Probe B (Stanford relativity gyroscope experiment to measure the Lense–Thirring effect to 1%) was launched and has been accumulating science data for more than 170 days now. μSCOPE (MICROSCOPE: MICRO-Satellite à trainée Compensée pour l'Observation du Principle d'Équivalence) is on its way for a 2008 launch to test Galileo equivalence principle to 10-15. LISA Pathfinder (SMART2), the technological demonstrator for the LISA (Laser Interferometer Space Antenna) mission is well on its way for a 2009 launch. STEP (Satellite Test of Equivalence Principle), and ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) are in good planning stage. Various astrophysical tests and cosmological tests of relativistic gravity will reach precision and ultra-precision stages. Clock tests and atomic interferometry tests of relativistic gravity will reach an ever-increasing precision. These will give revived interest and development both in experimental and theoretical aspects of gravity, and may lead to answers to some profound questions of gravity and the cosmos.
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MYRZAKULOV, R., L. SEBASTIANI, and S. ZERBINI. "SOME ASPECTS OF GENERALIZED MODIFIED GRAVITY MODELS." International Journal of Modern Physics D 22, no. 08 (June 21, 2013): 1330017. http://dx.doi.org/10.1142/s0218271813300176.
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In this paper, we review some general aspects of modified gravity theories, investigating mathematical and physical properties and, more specifically, the feature of viable and realistic models able to reproduce the dark energy (DE) epoch and the early-time inflation. We will discuss the black hole (BH) solutions in generalized theories of gravity: it is of fundamental interest to understand how properties and laws of BHs in General Relativity (GR) can be addressed in the framework of modified theories. In particular, we will discuss the energy issue and the possibility to derive the First Law of thermodynamics from the field equations. Then, in the analysis of cosmological solutions, we will pay particular attention to the occurrence of finite-time future singularities and to the possibility to avoid them in [Formula: see text]-gravity. Furthermore, realistic models of F(R)-gravity will be analyzed in detail. A general feature occurring in matter era will be shown, namely, the high derivatives of Hubble parameter may be influenced by the high frequency oscillation of the DE and some correction term may be required in order to stabilize the theory at high redshift. The inflationary scenario is also carefully analyzed and a unified description of the universe is evolved. In the final part of the work, we will look at the last developments in modified gravity, namely, we will investigate cosmological and BH solutions in a covariant field theory of gravity and we will introduce the extended "teleparallel" F(T)-gravity theories. A nice application to the dark matter (DM) problem will be presented.
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MASHHOON, BAHRAM. "BEYOND GRAVITOELECTROMAGNETISM: CRITICAL SPEED IN GRAVITATIONAL MOTION." International Journal of Modern Physics D 14, no. 12 (December 2005): 2025–37. http://dx.doi.org/10.1142/s0218271805008121.
Повний текст джерелаАнотація:
A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity is due to the existence of a critical speed. The dynamics of particles moving faster than the critical speed could then be contrary to Newtonian expectations. Working within the framework of gravitoelectromagnetism, the implications of the existence of a critical speed are explored. The results are expected to be significant for high energy astrophysics.
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Belinchón, José Antonio, та Rafael Uribe. "A comparative study of some cosmological models with time varying G and Λ: A symmetry approach". Canadian Journal of Physics 97, № 10 (жовтень 2019): 1083–95. http://dx.doi.org/10.1139/cjp-2018-0842.
Повний текст джерелаАнотація:
We study how the constants G and Λ may vary in four different theoretical models: general relativity with time-varying constants (Y.-K. Lau. Aust. J. Phys. 38, 547 (1985). doi: 10.1071/PH850547 ), the model proposed by Lu et al. (Phys Rev D, 89, 063526 (2014). doi: 10.1103/PhysRevD.89.063526 ), the model proposed by Bonanno et al. (Class. Quant. Grav. 24, 1443 (2007). doi: 10.1088/0264-9381/24/6/005 ), and the Brans–Dicke model with Λ([Formula: see text]) [ 25 ]. To carry out this study, we work under the self-similar hypothesis and we assume the same metric, a flat Friedmann–Robertson–Walker metric, and the same matter source, a perfect fluid. We put special emphasis on mathematical and formal aspects, which allows us to calculate exact power-law solutions through symmetry methods, matter collineation, and Noether symmetries. This enables us to compare the solutions of each model and in the same way to contrast the results with some observational data.
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Gupta, Rohit K., Supriya Kar, and R. Nitish. "Aspects of gravitational wave/particle duality: Bulk torsion ↔boundary gravity correspondence." International Journal of Modern Physics D 29, no. 02 (January 2020): 2050019. http://dx.doi.org/10.1142/s0218271820500194.
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A geometric torsion (GT) underlying a [Formula: see text]-form in a [Formula: see text]-dimensional [Formula: see text] gauge theory is revisited with a renewed perspective for a nonperturbation (NP) gravity in [Formula: see text]. In this context, we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a [Formula: see text] coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is identified as a mass dipole and is shown to be sourced by a propagating GT. A detailed analysis is performed in a bulk GT to show a modification to the precession of perihelion in a boundary NP gravity. The perspective of an electromagnetic (EM) wave in the bulk is investigated to reveal a spin [Formula: see text] (mass-less) quantum sourced by an apparent 2-form. A Goldstone scalar is absorbed by the apparent 2-form to describe a massive [Formula: see text]-form in the coulomb gauge. Alternately a Goldstone scalar together with a local degree of GT and 2-form is argued to govern a composite (mass-less) spin [Formula: see text] particle in Lorentz gauge. Both the scenarios, further ensure a graviton in a boundary NP gravity. A qualitative analysis reveals a (noninteracting) graviton underlying a plausible gravitational wave/particle duality in NP gravity.
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Beltrán Jiménez, Jose, Lavinia Heisenberg, and Tomi S. Koivisto. "The canonical frame of purified gravity." International Journal of Modern Physics D 28, no. 14 (October 2019): 1944012. http://dx.doi.org/10.1142/s0218271819440127.
Повний текст джерелаАнотація:
In the recently introduced gauge theory of translations, dubbed Coincident General Relativity (CGR), gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry and avoids the second derivatives that appear in the conventional Einstein–Hilbert action. While it implies the equivalent classical dynamics, the improved action principle can make a difference in considerations of energetics, thermodynamics and quantum theory. This paper reports on possible progress in those three aspects of gravity theory. In the so-called purified gravity, (1) energy–momentum is described locally by a conserved, symmetric tensor, (2) the Euclidean path integral is convergent without the addition of boundary or regulating terms and (3) it is possible to identify a canonical frame for quantization.
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RUFFINI, REMO, C. R. ARGÜELLES, B. M. O. FRAGA, A. GERALICO, H. QUEVEDO, J. A. RUEDA, and I. SIUTSOU. "BLACK HOLES IN GAMMA RAY BURSTS AND GALACTIC NUCLEI." International Journal of Modern Physics D 22, no. 11 (September 2013): 1360008. http://dx.doi.org/10.1142/s0218271813600080.
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Current research marks a clear success in identifying the moment of formation of a Black Hole of ~ 10M⊙, with the emission of a Gamma Ray Burst. This explains in terms of the 'Blackholic Energy' the source of the energy of these astrophysical systems. Their energetics up to 1054 erg, make them detectable all over our Universe. Concurrently a new problematic has been arising related to: (a) The evidence of Dark Matter in galactic halos; (b) The origin of the Super Massive Black Holes in active galactic nuclei and Quasars and (c) The purported existence of a Black Hole in the Center of our Galaxy. These three aspects of this new problematic have been traditionally approached independently. We propose an unified approach to all three of them based on a system of massive self-gravitating neutrinos in General Relativity. Perspectives of future research are presented.
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Brumberg, V. A., J. Henrard, Ju V. Batrakov, K. B. Bhatnagar, J. Chapront, A. Deprit, S. Ferraz-Mello, et al. "7 - Mecanique Celeste (Celestial Mechanics)." Transactions of the International Astronomical Union 20, no. 1 (1988): 15–28. http://dx.doi.org/10.1017/s0251107x0000688x.
Повний текст джерелаАнотація:
During 1985-1987 Celestial Mechanics has been intensively developed in all its branches embracing physical bases, mathematical aspects, computational techniques and astronomical objectives. Commission 7 has organized three IAU conferences: Symposium No. 114 “Relativity in Celestial Mechanics and Astrometry” (Leningrad, May 1985), Colloquium No. 96 “The Few Body Problem” (Turku, June 1987) and Topical Session “Resonances in the Solar System” of the X-th European Regional Astronomy Meeting (Prague, August 1987). Members of the commission have broadly participated in the NATO Advanced Study Institute “Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems” (Cortina d’Ampezzo, August 1987) and some other international and regional conferences. Prospects of the actual celestial mechanics investigations have been discussed at a session of Commission 7 at the XIX-th IAU General Assembly (New Delhi, November 1985). Three papers dealing with the unsolved problems of celestial mechanics were primarily addressed to the rising generation of celestial mechanicians (V. A. Brumberg and J. Kovalevsky, CM. 39, 133, 1986; P.K. Seidelmann, CM. 39, 141, 1986).
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Lalli, Roberto. "‘Dirty work’, but someone has to do it: Howard P. Robertson and the refereeing practices of Physical Review in the 1930s." Notes and Records: the Royal Society Journal of the History of Science 70, no. 2 (January 27, 2016): 151–74. http://dx.doi.org/10.1098/rsnr.2015.0022.
Повний текст джерелаАнотація:
In the 1930s the mathematical physicist Howard P. Robertson was the main referee of the journal Physical Review for papers concerning general relativity and related subjects. The rich correspondence between Robertson and the editors of the journal enables a historical investigation of the refereeing process of Physical Review at the time that it was becoming one of the most influential physics periodicals in the world. By focusing on this case study, the paper investigates two complementary aspects of the evolution of the refereeing process: first, the historical evolution of the refereeing practices in connection with broader contextual changes, and second, the attempts to define the activity of the referee, including the epistemic virtues required and the journal's functions according to the participants' categories. By exploring the tension between Robertson's idealized picture about how the referee should behave and the desire to promote his intellectual agenda, I show that the evaluation criteria that Robertson employed were contextually dependent and I argue that, in the 1930s, through his reports the referee had an enormous power in defining what direction future research should take.
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BARCELÓ, CARLOS, STEFANO LIBERATI, and MATT VISSER. "ANALOGUE MODELS FOR FRW COSMOLOGIES." International Journal of Modern Physics D 12, no. 09 (October 2003): 1641–49. http://dx.doi.org/10.1142/s0218271803004092.
Повний текст джерелаАнотація:
It is by now well known that various condensed matter systems may be used to mimic many of the kinematic aspects of general relativity, and in particular of curved-spacetime quantum field theory. In this essay we will take a look at what would be needed to mimic a cosmological spacetime — to be precise a spatially flat FRW cosmology — in one of these analogue models. In order to do this one needs to build and control suitable time dependent systems. We discuss here two quite different ways to achieve this goal. One might rely on an explosion, physically mimicking the big bang by an outflow of whatever medium is being used to carry the excitations of the analogue model, but this idea appears to encounter dynamical problems in practice. More subtly, one can avoid the need for any actual physical motion (and avoid the dynamical problems) by instead adjusting the propagation speed of the excitations of the analogue model. We shall focus on this more promising route and discuss its practicality.
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Zhu, Ben-Chao, and Xiang-Song Chen. "Tensor gauge condition and tensor field decomposition." Modern Physics Letters A 30, no. 35 (October 28, 2015): 1550192. http://dx.doi.org/10.1142/s0217732315501928.
Повний текст джерелаАнотація:
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin [Formula: see text]. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
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Riazuelo, Alain. "Seeing relativity-I: Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars." International Journal of Modern Physics D 28, no. 02 (January 2019): 1950042. http://dx.doi.org/10.1142/s0218271819500421.
Повний текст джерелаАнотація:
We present an implementation of a ray tracing code in the Schwarzschild metric. We aim at building a numerical code with a correct implementation of both special (aberration, amplification and Doppler) and general (deflection of light, lensing and gravitational redshift) relativistic effects so as to simulate what an observer with arbitrary velocity would see near, or possibly within, the black hole. We also pay some specific attention to perform a satisfactory rendering of stars. Using this code, we then show several unexplored features of the maximal analytical extension of the metric. In particular, we study the aspect of the second asymptotic region of the metric as seen by an observer crossing the horizon. We also address several aspects related to the white hole region (i.e. past singularity) seen both from outside the black hole, inside the future horizon and inside the past horizon, which gives rise to the most counter-intuitive effects.
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ANDERSON, EDWARD. "RELATIONAL QUADRILATERALLAND I: THE CLASSICAL THEORY." International Journal of Modern Physics D 23, no. 02 (January 29, 2014): 1450014. http://dx.doi.org/10.1142/s021827181450014x.
Повний текст джерелаАнотація:
Relational particle mechanics models bolster the relational side of the absolute versus relational motion debate. They are additionally toy models for the dynamical formulation of general relativity (GR) and its problem of time (PoT). They cover two aspects that the more commonly studied minisuperspace GR models do not: (1) by having a nontrivial notion of structure and thus of cosmological structure formation and of localized records. (2) They have linear as well as quadratic constraints, which is crucial as regards modeling many PoT facets. I previously solved relational triangleland classically, quantum mechanically and as regards a local resolution of the PoT. This rested on triangleland's shape space being 𝕊2with isometry group SO(3), allowing for use of widely-known geometry, methods and atomic/molecular physics analogies. I now extend this work to the relational quadrilateral, which is far more typical of the general N-a-gon, represents a "diagonal to nondiagonal Bianchi IX minisuperspace" step-up in complexity, and encodes further PoT subtleties. The shape space now being ℂℙ2with isometry group SU(3)/ℤ3, I now need to draw on geometry, shape statistics and particle physics to solve this model; this is therefore an interdisciplinary paper. This Paper treats quadrilateralland at the classical level, and then paper II provides a quantum treatment.
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Roth, Yehuda. "Agility as the fundamental concept of classical mechanics." Physics Essays 34, no. 2 (June 9, 2021): 168–73. http://dx.doi.org/10.4006/0836-1398-34.2.168.
Повний текст джерелаАнотація:
In this paper, we introduce a mathematical formalism that demonstrates how concepts are implemented in physical theories, with a focus on the agility concept. We define a concept manifestation as a process, in which a concept is assigned to an object (e.g., a body or a particle). In the implementation stage, a physical theory is spanned, and we demonstrate how the implementation of the concept of agility generates the rules of classical mechanics and, in some aspects, general relativity. Using this approach, we show that both expressions for momentum— <mml:math display="inline"> <mml:mover accent="true"> <mml:mi>p</mml:mi> <mml:mo></mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mi>m</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mo></mml:mo> </mml:mover> </mml:mrow> <mml:mo></mml:mo> </mml:mover> </mml:math> and <mml:math display="inline"> <mml:mover accent="true"> <mml:mi>p</mml:mi> <mml:mo></mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="italic"></mml:mi> <mml:mo>/</mml:mo> <mml:mi>λ</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mo></mml:mo> </mml:mover> </mml:math> —originate from the same source-time derivative of an agility operator. We conclude that physical laws that can serve as representative concepts may be useful in artificial intelligence systems.
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LUCCHESI, DAVID M. "THE IMPACT OF THE EVEN ZONAL HARMONICS SECULAR VARIATIONS ON THE LENSE–THIRRING EFFECT MEASUREMENT WITH THE TWO LAGEOS SATELLITES." International Journal of Modern Physics D 14, no. 12 (December 2005): 1989–2023. http://dx.doi.org/10.1142/s0218271805008169.
Повний текст джерелаАнотація:
This work has been motivated by the criticisms raised on the error budget contribution — on a recently performed measurement of the Lense–Thirring effect — from the uncertainties of the secular variations of the Earth's even zonal harmonics. The relativistic secular precession has been observed from the analysis of 11 years of LAGEOS and LAGEOS II laser ranging data. In the analysis, the recent EIGEN–GRACE02S gravity field model (derived from GRACE data only) was used during the orbit determination process using the NASA Goddard software package GEODYN II. In particular, the measurement has been derived combining the nodes only of the two LAGEOS satellites in order to cancel the larger error source, due to the uncertainty of the first even zonal harmonic, and solved for the Lense–Thirring effect predicted by Einstein's general relativity. The authors of the relativistic measurement claimed an error of about 1% of the relativistic effect as due to the temporal variation of the even zonal harmonics. The main criticism is that on a much larger error estimate, about 11% of the relativistic effect on the analyzed time span of the two LAGEOS satellites orbital data should be considered. Moreover, the authors of the relativistic measurement emphasized that whatever the value they chose for the secular variations, in particular of the effective value for [Formula: see text], they always obtained the same discrepancy of about 1% between the observed and predicted effect, without however providing a detailed explanation. In the present work we address all the cited aspects. In particular, we explain the physical reason for the results obtained by the authors of the relativistic measurement in all their simulations. As we will see, two additional errors (linear in time) must be considered in the satellites orbit analysis if we want to correctly explain the experimental results. The first is a time-dependent error related with the mismodeling of the secular variations of the even zonal harmonics. The inclusion of this error in the error analysis explains why the same discrepancy between the observed and predicted effect has been always obtained independently of the assumed value for [Formula: see text], i.e. for the errors in the time variations of the even zonal harmonics. The second is a time-independent error related to the non-coincidence between the reference epoch of the gravity field, i.e. the middle epoch of the time span during which the gravity field has been determined by the GRACE mission, and the reference epoch fixed in the orbit analysis program. The inclusion of this error in the error analysis explains the 1% value for the discrepancy between the prediction and the observations. In order to validate our results we fitted for an effective [Formula: see text] from the combined nodes of the LAGEOS satellites with the EIGEN2S gravity field model obtained from the CHAMP mission. From our fit, we consistently confirmed our previous statements. In particular, we prove a very interesting and new approach in order to compute the effective values of the time variations of the even zonal harmonics from the estimate of the time-independent error previously cited.
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BOI, LUCIANO. "IDEAS OF GEOMETRIZATION, GEOMETRIC INVARIANTS OF LOW-DIMENSIONAL MANIFOLDS, AND TOPOLOGICAL QUANTUM FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 06, no. 05 (August 2009): 701–57. http://dx.doi.org/10.1142/s0219887809003783.
Повний текст джерелаАнотація:
The aim of the first part of this paper is to make some reflections on the role of geometrical and topological concepts in the developments of theoretical physics, especially in gauge theory and string theory, and we show the great significance of these concepts for a better understanding of the dynamics of physics. We will claim that physical phenomena essentially emerge from the geometrical and topological structure of space–time. The attempts to solve one of the central problems in 20th theoretical physics, i.e. how to combine gravity and the other forces into an unitary theoretical explanation of the physical world, essentially depends on the possibility of building a new geometrical framework conceptually richer than Riemannian geometry. In fact, it still plays a fundamental role in non-Abelian gauge theories and in superstring theory, thanks to which a great variety of new mathematical structures has emerged. The scope of this presentation is to highlight the importance of these mathematical structures for theoretical physics. A very interesting hypothesis is that the global topological properties of the manifold's model of space–time play a major role in quantum field theory (QFT) and that, consequently, several physical quantum effects arise from the nonlocal changing metrical and topological structure of these manifold. Thus the unification of general relativity and quantum theory require some fundamental breakthrough in our understanding of the relationship between space–time and quantum process. In particular the superstring theories lead to the guess that the usual structure of space–time at the quantum scale must be dropped out from physical thought. Non-Abelian gauge theories satisfy the basic physical requirements pertaining to the symmetries of particle physics because they are geometric in character. They profoundly elucidate the fundamental role played by bundles, connections, and curvature in explaining the essential laws of nature. Kaluza–Klein theories and more remarkably superstring theory showed that space–time symmetries and internal (quantum) symmetries might be unified through the introduction of new structures of space with a different topology. This essentially means, in our view, that "hidden" symmetries of fundamental physics can be related to the phenomenon of topological change of certain class of (presumably) nonsmooth manifolds. In the second part of this paper, we address the subject of topological quantum field theories (TQFTs), which constitute a remarkably important meeting ground for physicists and mathematicians. TQFTs can be used as a powerful tool to probe geometry and topology in low dimensions. Chern–Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of QFTs which can be exactly (nonperturbatively) and explicitly solved. Abelian Chern–Simons theory provides a field theoretic interpretation of the linking and self-linking numbers of a link (i.e. the union of a finite number of disjoint knots). In non-Abelian theories, vacuum expectation values of Wilson link operators yield a class of polynomial link invariants; the simplest of them is the well-known Jones polynomial. Powerful methods for complete analytical and nonperturbative computation of these knot and link invariants have been developed. From these invariants for unoriented and framed links in S3, an invariant for any three-manifold can be easily constructed by exploiting the Lickorish–Wallace surgery presentation of three-manifolds. This invariant up to a normalization is the partition function of the Chern–Simons field theory. Even perturbative analysis of Chern–Simons theories are rich in their mathematical structure; these provide a field theoretic interpretation of Vassiliev knot invariants. In Donaldson–Witten theory perturbative methods have proved their relations to Donaldson invariants. Nonperturbative methods have been applied after the work by Seiberg and Witten on N = 2 supersymmetric Yang–Mills theory. The outcome of this application is a totally unexpected relation between Donaldson invariants and a new set of topological invariants called Seiberg–Witten invariants. Not only in mathematics, Chern–Simons theories find important applications in three- and four-dimensional quantum gravity also. Work on TQFT suggests that a quantum gravity theory can be formulated in three-dimensional space–time. Attempts have been made in the last years to formulate a theory of quantum gravity in four-dimensional space–time using "spin networks" and "spin foams". More generally, the developments of TQFTs represent a sort of renaissance in the relation between geometry and physics. The most important (new) feature of present developments is that links are being established between quantum physics and topology. Maybe this link essentially rests on the fact that both quantum theory and topology are characterized by discrete phenomena emerging from a continuous background. One very interesting example is the super-symmetric quantum mechanics theory, which has a deep geometric meaning. In the Witten super-symmetric quantum mechanics theory, where the Hamiltonian is just the Hodge–Laplacian (whereas the quantum Hamiltonian corresponding to a classical particle moving on a Riemannian manifold is just the Laplace–Beltrami differential operator), differential forms are bosons or fermions depending on the parity of their degrees. Witten went to introduce a modified Hodge–Laplacian, depending on a real-valued function f. He was then able to derive the Morse theory (relating critical points of f to the Betti numbers of the manifold) by using the standard limiting procedures relating the quantum and classical theories. Super-symmetric QFTs essentially should be viewed as the differential geometry of certain infinite-dimensional manifolds, including the associated analysis (e.g. Hodge theory) and topology (e.g. Betti numbers). A further comment is that the QFTs of interest are inherently nonlinear, but the nonlinearities have a natural origin, e.g. coming from non-Abelian Lie groups. Moreover there is usually some scaling or coupling parameter in the theory which in the limit relates to the classical theory. Fundamental topological aspects of such a quantum theory should be independent of the parameters and it is therefore reasonable to expect them to be computable (in some sense) by examining the classical limit. This means that such topological information is essentially robust and should be independent of the fine analytical details (and difficulties) of the full quantum theory. In the last decade much effort has been done to use these QFTs as a conceptual tool to suggest new mathematical results. In particular, they have led to spectacular progress in our understanding of geometry in low dimensions. It is most likely no accident that the usual QFTs can only be renormalized in (space–time) dimensions ≤4, and this is precisely the range in which difficult phenomena arise leading to deep and beautiful theories (e.g. the work of Thurston in three dimensions and Donaldson in four dimensions). It now seems clear that the way to investigate the subtleties of low-dimensional manifolds is to associate to them suitable infinite-dimensional manifolds (e.g. spaces of connections) and to study these by standard linear methods (homology, etc.). In other words we use QFT as a refined tool to study low-dimensional manifolds.
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Chrusciel, Piotr, James Isenberg, and Alan Rendall. "Mathematical Aspects of General Relativity." Oberwolfach Reports, 2006, 73–118. http://dx.doi.org/10.4171/owr/2006/02.
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Chruściel, Piotr, James Isenberg, and Alan Rendall. "Mathematical Aspects of General Relativity." Oberwolfach Reports, 2009, 2585–646. http://dx.doi.org/10.4171/owr/2009/46.
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Denis, Olivier. "Entropic Information Theory: Formulae and Quantum Gravity Bits from Bit." Physical Science International Journal, December 13, 2021, 23–30. http://dx.doi.org/10.9734/psij/2021/v25i930281.
Повний текст джерелаАнотація:
We show here that entropic information is capable of unifying all aspects of the universe at all scales in a coherent and global theoretical mathematical framework materialized by entropic information framework, theory and formulas, where dark matter, dark energy and gravity are truly informationals processes and where information is code and code is what creates the process, it is itself the process. Mass, energy and movement of information are respectively dark matter, dark energy, and gravity. Here, we reconcile general relativity and quantum mechanics by introducing quantum gravity for the Planckian scale. The formulas of entropic information are expressed in natural units, physical units of measurement based only on universal constants, constants, which refer to the basic structure of the laws of physics: C and G are part of the structure of space-time in general relativity, and h captures the relationship between energy and frequency that is the basis of quantum mechanics. Here we show that entropic information formulas are able to present entropic information in various unifying aspects and introduce gravity at the Planck scale. We prove that Entropic information theory is thus building the bridge between general relativity and quantum mechanics
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Tripathy, S. K., B. Mishra, Maxim Khlopov, and Saibal Ray. "Cosmological models with a hybrid scale factor." International Journal of Modern Physics D, June 15, 2021, 2140005. http://dx.doi.org/10.1142/s0218271821400058.
Повний текст джерелаАнотація:
In this paper, we present some cosmological models with a hybrid scale factor (HSF) in the framework of general relativity (GR). The HSF fosters an early deceleration as well as a late-time acceleration and mimics the present Universe. The dynamical aspects of different cosmological models with HSF in the presence of different matter fields have been discussed.
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Bjerrum-Bohr, N. Emil J., Poul Henrik Damgaard, Ludovic Planté, and Pierre Vanhove. "The SAGEX Review on scattering amplitudes, Chapter 13: Post-Minkowskian expansion from scattering amplitudes." Journal of Physics A: Mathematical and Theoretical, June 20, 2022. http://dx.doi.org/10.1088/1751-8121/ac7a78.
Повний текст джерелаАнотація:
Abstract The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein-Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years.
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Dias, F. S., G. B. Santos, L. G. Gomes, and L. F. Mello. "The power-law dependence between the matter-radiation and Hubble anisotropies." International Journal of Modern Physics D, April 18, 2022. http://dx.doi.org/10.1142/s0218271822500493.
Повний текст джерелаАнотація:
In this paper, we investigate the cosmological evolution of the Hubble and the matter-radiation anisotropies, characterized by [Formula: see text] and [Formula: see text], respectively, under the power-law condition [Formula: see text]. This is a suitable choice in order to understand how different [Formula: see text] and [Formula: see text] would behave in the expanding universe if they had distinct orders of magnitude. Hence, their early and late-time behaviors are examined, and in particular, the dependence of their qualitative features on [Formula: see text]. This includes some nontrivial aspects in their long-time dynamics, which goes beyond the reach of the linear perturbations of the homogeneous and isotropic models. Besides those cosmological concerns, the concept of anisotropy in general relativity and its counterpart in Einstein’s equations is clarified and interpreted, and the general notion of the Kasner plane, the arena where its dynamics takes place, is extended beyond the reach of the spatially homogeneous models.
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Dadhich, Naresh. "On space–time structure and the Universe: some issues of concept and principle." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, no. 2230 (July 4, 2022). http://dx.doi.org/10.1098/rsta.2021.0405.
Повний текст джерелаАнотація:
In this discourse, we would like to discuss some issues of concept and principle in the context of the following three aspects. One, how Λ arises as a constant of space–time structure on the same footing as the velocity of light. These are the two constants innate to space–time without reference to any force or dynamics whatsoever, and are interwoven in the geometry of ‘free’ homogeneous space–time. Two, how does the vacuum energy gravitate? Could its gravitational interaction in principle be included in general relativity or a new theory of quantum space–time/gravity would be required? Finally, we would like to raise the fundamental question: How does the Universe physically expand? Since there does not lie anything outside into which it can expand, instead it has to expand on its own—maybe by creating new space–time out of nothing at each instant and at every location! Thus not only was the Universe created at some instant in the past marking the beginning in the Big Bang, it is in fact being created continuously at each epoch as it expands. We thus need quantum theory of space–time/gravity for fully understanding the working of the Universe. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.
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Javed, Faisal, Sobia Sadiq, Ghulam Mustafa, and Ibrar Hussain. "A comparative study of new generic wormhole models with stability analysis via thin-shell." Physica Scripta, November 3, 2022. http://dx.doi.org/10.1088/1402-4896/ac9ff6.
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Abstract This analysis is devoted to exploring the interesting aspects of wormhole geometry. The energy conditions are checked for two different new generic shape functions, which satisfy the required wormhole properties. The presence of exotic matter is confirmed due to the violation of the energy conditions in the background of f(R, T ) gravity as well as in the general relativity case. The traversable wormholes respecting the null energy conditions can be realized in both considered frameworks. A thin-shell around a wormhole geometry with two different generic shape functions is obtained by using the cut and paste approach taking Schwarzschild spacetime as an exterior manifold. The stability of thin-shell is explored with linearized perturbation along the equilibrium shell radius. Stable regions and the position of the expected event horizon depend on the choice of physical parameters. It is concluded that the number of expected event horizons increases for the second shape function.
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Bhattacharjee, Deep. "M-Theory and F-Theory over Theoretical Analysis on Cosmic Strings and Calabi-Yau Manifolds Subject to Conifold Singularity with Randall-Sundrum Model." Asian Journal of Research and Reviews in Physics, July 15, 2022, 25–40. http://dx.doi.org/10.9734/ajr2p/2022/v6i230181.
Повний текст джерелаАнотація:
String theory always comes with heavy mathematical rigor as it questions the most significant and impossible attempt to make a scale-invariant phenomenology between general relativity and quantum theory. Thus, steps have been taken to simplify the theory a bit thereby making it accessible to general yet enthusiastic readers of physics. However, as there is numerous mathematics involved in the modeling of this theory, thus, any chance to make a purely non-mathematical approach towards strings would prove vacuous and intimidating making the pathway of this marvelous theory chocked with unnecessary assumptions resulting in false analogies (or hopes) relating to this theory. Thus, where it’s almost impossible to proceed without any equations, we have given a few just to wipe out some logical confusion arising to the first readers of strings. Few necessary diagrams are included along with intense theory and least mathematics for making this significant approach of theoretical physicists accessible to general learners or readers.
Topics: Bosonic string theory, supersymmetric string theory, M – theory, F – theory, dualities and interconnectedness, viability, Randall – Sundrum model for tackling the hierarchy problem of particle physics, conifold singularities, Branes, Bulks, Extremal black holes, Ekpyrotic cosmology, topological aspects of Calabi – Yau (CY) manifolds, A and B models, Mirror Symmetries; AdS/CFT, cosmic strings, all in a way accessible to every reader.
Methods: Theoretical analogies, deductions, principles behind the origin, development along with the probable conclusion of this theory, the roots of its origin, the necessary difficulty for detecting those strings, and approaches done by theorists to work out the pathway of achieving Einstein’s dream of unification irrespective of several hindrances.
Results: String theory itself is not a complete theory. Rather it’s in the process of further development through the increment of time resulting in more applications of mathematics by developing or incorporating them in due needs. Thus, without stating any concrete results, the theory has been tackled in this paper with a viable hypothesis based on the current understanding, and previous attempts are stated to have been made for its success.
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Salucci, Paolo, Giampiero Esposito, Gaetano Lambiase, Emmanuele Battista, Micol Benetti, Donato Bini, Lumen Boco, et al. "Einstein, Planck and Vera Rubin: Relevant Encounters Between the Cosmological and the Quantum Worlds." Frontiers in Physics 8 (February 16, 2021). http://dx.doi.org/10.3389/fphy.2020.603190.
Повний текст джерелаАнотація:
In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these “paths or contamination” beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges. Finally, a very complete and accurate bibliography is provided to help the reader in navigating all these issues.
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Capozziello, Salvatore, and Francesco Bajardi. "Nonlocal gravity cosmology: An overview." International Journal of Modern Physics D, December 15, 2021. http://dx.doi.org/10.1142/s0218271822300099.
Повний текст джерелаАнотація:
We discuss some main aspects of theories of gravity containing nonlocal terms in view of cosmological applications. In particular, we consider various extensions of general relativity based on geometrical invariants as [Formula: see text], [Formula: see text] and [Formula: see text] gravity where [Formula: see text] is the Ricci curvature scalar, [Formula: see text] is the Gauss–Bonnet topological invariant, [Formula: see text] the torsion scalar and the operator [Formula: see text] gives rise to nonlocality. After selecting their functional form by using Noether symmetries, we find out exact solutions in a cosmological background. It is possible to reduce the dynamics of selected models and to find analytic solutions for the equations of motion. As a general feature of the approach, it is possible to address the accelerated expansion of the Hubble flow at various epochs, in particular the dark energy issues, by taking into account nonlocality corrections to the gravitational Lagrangian. On the other hand, it is possible to search for gravitational nonlocal effects also at astrophysical scales. In this perspective, we search for symmetries of [Formula: see text] gravity also in a spherically symmetric background and constrain the free parameters, Specifically, by taking into account the S2 star orbiting around the Galactic Center SgrA[Formula: see text], it is possible to study how nonlocality affects stellar orbits around such a massive self-gravitating object.
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López-Corredoira, Martín, and Louis Marmet. "Alternative ideas in cosmology." International Journal of Modern Physics D, March 18, 2022. http://dx.doi.org/10.1142/s0218271822300142.
Повний текст джерелаАнотація:
Some remarkable examples of alternative cosmological theories are reviewed here, ranging from a compilation of variations on the Standard Model through the more distant quasi-steady-state cosmology, plasma cosmology, or universe models as a hypersphere, to the most exotic cases including static models. The present-day Standard Model of cosmology, [Formula: see text]CDM, gives us a representation of a cosmos whose dynamics is dominated by gravity (Friedmann equations derived from general relativity) with a finite lifetime, large scale homogeneity, expansion and a hot initial state, together with other elements necessary to avoid certain inconsistencies with observations (inflation, nonbaryonic dark matter, dark energy, etc.). There are however some models with characteristics that are close to those of the Standard Model but differing in some minor aspects; we call these “variations on the Standard Model”. Many of these models are indeed investigated by some mainstream cosmologists: different considerations on CP violation, inflation, number of neutrino species, quark-hadron phase transition, baryonic or nonbaryonic dark-matter, dark energy, nucleosynthesis scenarios, large-scale structure formation scenarios; or major variations like a inhomogeneous universe, Cold Big Bang, varying physical constants or gravity law, zero-active mass (also called “[Formula: see text]”), Milne, and cyclical models. At the most extreme distance from the Standard Model, the static models, a noncosmological redshift includes “tired-light” hypotheses, which assume that the photon loses energy owing to an intrinsic property or an interaction with matter or light as it travels some distance, or other nonstandard ideas. Our impression is that none of the alternative models has acquired the same level of development as [Formula: see text]CDM in offering explanations of available cosmological observations. One should not, however, judge any theory in terms of the number of observations that it can successfully explain (ad hoc in many cases) given the much lower level of development of the alternative ones, but by the plausibility of its principles and its potential to fit data with future improvements of the theories. A pluralist approach to cosmology is a reasonable option when the preferred theory is still under discussion.