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Journal articles on the topic 'Gravity Tensor'

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Author: Grafiati

Published: 11 March 2023

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1

POPŁAWSKI, NIKODEM J. "ON THE NONSYMMETRIC PURELY AFFINE GRAVITY." Modern Physics Letters A 22, no. 36 (November 30, 2007): 2701–20. http://dx.doi.org/10.1142/s0217732307025662.

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We review the vacuum purely affine gravity with the nonsymmetric connection and metric. We also examine dynamical effects of the second Ricci tensor and covariant second-rank tensors constructed from the torsion tensor in the gravitational Lagrangian.

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2

Gogberashvili, M. Y. "Tensor-tensor model of gravity." Theoretical and Mathematical Physics 113, no. 3 (December 1997): 1572–81. http://dx.doi.org/10.1007/bf02634517.

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3

Bergshoeff, Eric, Wout Merbis, Alasdair J. Routh, and Paul K. Townsend. "The third way to 3D gravity." International Journal of Modern Physics D 24, no. 12 (October 2015): 1544015. http://dx.doi.org/10.1142/s0218271815440150.

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Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

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4

Torres, Diego F., and Héctor Vucetich. "Hyperextended scalar-tensor gravity." Physical Review D 54, no. 12 (December 15, 1996): 7373–77. http://dx.doi.org/10.1103/physrevd.54.7373.

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5

Chiba, Takeshi. "1/R gravity and scalar-tensor gravity." Physics Letters B 575, no. 1-2 (November 2003): 1–3. http://dx.doi.org/10.1016/j.physletb.2003.09.033.

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6

Nieto, J. A. "Alternative self-dual gravity in eight dimensions." Modern Physics Letters A 31, no. 26 (August 17, 2016): 1650147. http://dx.doi.org/10.1142/s0217732316501479.

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We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell–Mansouri physical framework and a self-dual curvature symmetry, we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein–Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.

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7

VERDAGUER, ENRIC. "METRIC FLUCTUATIONS IN DE SITTER SPACETIME IN STOCHASTIC GRAVITY." International Journal of Modern Physics D 20, no. 05 (May 20, 2011): 851–60. http://dx.doi.org/10.1142/s0218271811019189.

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Stochastic gravity extends semiclassical gravity by allowing for a systematic and self-consistent description of the metric fluctuations produced by the quantum fluctuations of the stress tensor. The effect of minimally coupled scalar fields with arbitrary mass in de Sitter spacetime is discussed, assuming that these fields are in the Bunch–Davies de Sitter invariant vacuum. The matter field fluctuations are described by the noise kernel which is obtained from the symmetrized two-point correlation of the stress tensor operator. The noise kernel is computed in terms of de Sitter invariant bi-tensors. It turns out that in a de Sitter background the two-point function of the linearized Einstein tensor, which is gauge invariant, is directly related to the noise kernel.

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8

Peng, Jun-Jin, and Hui-Fa Liu. "A new formula for conserved charges of Lovelock gravity in AdS space–times and its generalization." International Journal of Modern Physics A 35, no. 20 (July 2, 2020): 2050102. http://dx.doi.org/10.1142/s0217751x2050102x.

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Within the framework of the Lovelock gravity theory, we propose a new rank-four divergenceless tensor consisting of the Riemann curvature tensor and inheriting its algebraic symmetry characters. Such a tensor can be adopted to define conserved charges of the Lovelock gravity theory in asymptotically anti-de Sitter (AdS) space–times. Besides, inspired with the case of the Lovelock gravity, we put forward another general fourth-rank tensor in the context of an arbitrary diffeomorphism invariant theory of gravity described by the Lagrangian constructed out of the curvature tensor. On basis of the newly-constructed tensor, we further suggest a Komar-like formula for the conserved charges of this generic gravity theory.

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9

Heisenberg, Lavinia. "Scalar-vector-tensor gravity theories." Journal of Cosmology and Astroparticle Physics 2018, no. 10 (October 29, 2018): 054. http://dx.doi.org/10.1088/1475-7516/2018/10/054.

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10

Moffat, J. W. "Scalar–tensor–vector gravity theory." Journal of Cosmology and Astroparticle Physics 2006, no. 03 (March 6, 2006): 004. http://dx.doi.org/10.1088/1475-7516/2006/03/004.

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11

Chkareuli, J. L., C. D. Froggatt, and H. B. Nielsen. "Spontaneously generated tensor field gravity." Nuclear Physics B 848, no. 3 (July 2011): 498–522. http://dx.doi.org/10.1016/j.nuclphysb.2011.03.009.

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12

Zhang, Changyou, Martin F. Mushayandebvu, Alan B. Reid, J. Derek Fairhead, and Mark E. Odegard. "Euler deconvolution of gravity tensor gradient data." GEOPHYSICS 65, no. 2 (March 2000): 512–20. http://dx.doi.org/10.1190/1.1444745.

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Tensor Euler deconvolution has been developed to help interpret gravity tensor gradient data in terms of 3-D subsurface geological structure. Two forms of Euler deconvolution have been used in this study: conventional Euler deconvolution using three gradients of the vertical component of the gravity vector and tensor Euler deconvolution using all tensor gradients. These methods have been tested on point, prism, and cylindrical mass models using line and gridded data forms. The methods were then applied to measured gravity tensor gradient data for the Eugene Island area of the Gulf of Mexico using gridded and ungridded data forms. The results from the model and measured data show significantly improved performance of the tensor Euler deconvolution method, which exploits all measured tensor gradients and hence provides additional constraints on the Euler solutions.

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13

Abdelmohssin, Faisal A. Y., and Osman M. H. El Mekki. "The Hamiltonian of f(R) gravity." Canadian Journal of Physics 99, no. 9 (September 2021): 814–19. http://dx.doi.org/10.1139/cjp-2021-0058.

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We derive conjugate momenta variable tensors and the Hamiltonian equation of the source-free f(R) gravity from first principles using the Legendre transformation of these conjugate momenta variable tensors, conjugate coordinates variables — fundamental metric tensor and its first ordinary partial derivatives with respect to space–time coordinates and second ordinary partial derivatives with respect to space–time coordinates — and the Lagrangian of the f(R) gravity. Interpreting the derived Hamiltonian as the energy of the f(R) gravity we have shown that it vanishes for linear Lagrangians in Ricci scalar curvature without source (e.g., Einstein–Hilbert Lagrangian without matter fields), which is the same result obtained using the stress–energy tensor equation derived from variation of the matter field Lagrangian density. The resulting Hamiltonian equation forbids any negative power law model in the dependence of the f(R) gravity on Ricci scalar curvature: f(R) = αR–r, where r and α are positive real numbers; it also forbids any polynomial equation that contains terms with negative powers of the Ricci scalar curvature including a constant term, in which cases the Hamiltonian function in the Ricci scalar and therefore the energy of the f(R) gravity would attain a negative value and would not be bounded from below. The restrictions imposed by the non-negative Hamiltonian have far-reaching consequences as a result of applying f(R) gravity to the study of black holes and the Friedmann–Lemaître–Robertson–Walker model in cosmology.

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14

KANEDA, SHO, SERGEI V. KETOV, and NATSUKI WATANABE. "FOURTH-ORDER GRAVITY AS THE INFLATIONARY MODEL REVISITED." Modern Physics Letters A 25, no. 32 (October 20, 2010): 2753–62. http://dx.doi.org/10.1142/s0217732310033918.

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We revisit the old (fourth-order or quadratically generated) gravity model of Starobinsky in four spacetime dimensions, and derive the (inflaton) scalar potential in the equivalent scalar–tensor gravity model. The inflaton scalar potential is used to compute the (CMB) observables of inflation, associated with curvature perturbations (namely, the scalar and tensor spectral indices, and the tensor-to-scalar ratio), including the new next-to-leading order terms with respect to the inverse number of e-foldings. The results are compared to the recent (WMAP5) experimental bounds. We confirm both mathematical and physical equivalence between f(R) gravity theories and the corresponding scalar–tensor gravity theories.

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15

Raziani, R., and M. V. Takook. "Polarization tensor in de Sitter gauge gravity." International Journal of Modern Physics D 30, no. 05 (February 25, 2021): 2150035. http://dx.doi.org/10.1142/s0218271821500358.

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The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

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16

HSU, JONG-PING. "YANG–MILLS GRAVITY IN FLAT SPACE–TIME I: CLASSICAL GRAVITY WITH TRANSLATION GAUGE SYMMETRY." International Journal of Modern Physics A 21, no. 25 (October 10, 2006): 5119–39. http://dx.doi.org/10.1142/s0217751x06034082.

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We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space–time with a new Yang–Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an "effective Riemann metric tensor" for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space–time. In the post-Newtonian approximation of the tensor gauge field produced by the energy–momentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

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17

POPŁAWSKI, NIKODEM J. "THE MAXWELL LAGRANGIAN IN PURELY AFFINE GRAVITY." International Journal of Modern Physics A 23, no. 03n04 (February 10, 2008): 567–79. http://dx.doi.org/10.1142/s0217751x08039578.

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The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein–Maxwell equations in the metric–affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell–Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.

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18

Abebe, Amare, and Maye Elmardi. "Irrotational-fluid cosmologies in fourth-order gravity." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550118. http://dx.doi.org/10.1142/s0219887815501182.

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In this paper, we explore classes of irrotational-fluid cosmological models in the context of f(R)-gravity in an attempt to put some theoretical and mathematical restrictions on the form of the f(R) gravitational Lagrangian. In particular, we investigate the consistency of linearized dust models for shear-free cases as well as in the limiting cases when either the gravito-magnetic or gravito-elecric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in f(R)-gravity.

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19

Pajot, G., O. de Viron, M. Diament, M. F. Lequentrec-Lalancette, and V. Mikhailov. "Noise reduction through joint processing of gravity and gravity gradient data." GEOPHYSICS 73, no. 3 (May 2008): I23—I34. http://dx.doi.org/10.1190/1.2905222.

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In mineral and oil exploration, gravity gradient data can help to delineate small-scale features that cannot be retrieved from gravity measurements. Removing high-frequency noise while preserving the high-frequency real signal is one of the most challenging tasks associated with gravity gradiometry data processing. We present a method to reduce gravity and gravity gradient data noise when both are measured in the same area, based on a least-squares simultaneous inversion of observations and physical constraints, inferred from the gravity gradient tensor definition and its mathematical properties. Instead of handling profiles individually, our noise-reduction method uses simultaneously measured values of the tensor components and of gravity in the whole survey area, benefiting from all available information. Synthetic examples show that more than half of the random noise can be removed from all tensor components and nearly all the noise from the gravity anomaly without altering the high-frequency information. We apply our method to a set of marine gravity gradiometry data acquired by Bell Geospace in the Faroe-Shetland Basin to demonstrate its power to resolve small-scale features.

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20

CAPOZZIELLO, S., and M. DE LAURENTIS. "GRAVITY FROM LOCAL POINCARÉ GAUGE INVARIANCE." International Journal of Geometric Methods in Modern Physics 06, no. 01 (February 2009): 1–24. http://dx.doi.org/10.1142/s0219887809003400.

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A compact, self-contained approach to gravitation, based on the local Poincaré gauge invariance, is proposed. Starting from the general invariance principle, we discuss the global and the local Poincaré invariance developing the spinor, vector and tetrad formalisms. These tools allow to construct the curvature, torsion and metric tensors by the Fock–Ivanenko covariant derivative. The resulting Einstein–Cartan theory describes a space endowed with non-vanishing curvature and torsion while the gravitational field equations are similar to the Yang–Mills equations of motion with the torsion tensor playing the role of the Yang–Mills field strength.

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21

Li, Yaoguo. "Understanding curvatures of the equipotential surface in gravity gradiometry." GEOPHYSICS 83, no. 4 (July 1, 2018): G35—G45. http://dx.doi.org/10.1190/geo2017-0612.1.

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The concept of curvatures of equipotential surfaces is of theoretical and practical importance in gravity gradiometry because curvatures describe the shape of equipotential surfaces, which can yield information about the shape of the source. Although the fundamentals of curvatures are well-established, their connection to modern gravity gradiometry and the associated applications in exploration geophysics remain areas of active research. In particular, there is a misunderstanding in the calculation of the said curvatures directly from measured gravity gradient data that are now widely used in exploration geophysics. The error stems from the incorrect use of the formulas in a fixed user coordinate system that are only valid in a rotated coordinate system. We demonstrate that the gravity gradient tensor must be rotated to a local coordinate system whose vertical axis is aligned with the local anomalous gravity field direction so that the curvatures of the anomalous equipotential surface can be calculated correctly using these classic formulas. To facilitate practical application, we present theoretical and practical aspects related to coordinate systems and rotations of the gravity gradient tensor. We have also developed an approach for estimating local gravity for use in the curvature calculation by wavenumber-domain conversion from gradient tensors. The procedure may form a basis for developing new interpretation techniques in gravity gradient gradiometry based on curvatures.

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22

Cevallos, Carlos. "Interpreting the direction of the gravity gradient tensor eigenvectors: Their relation to curvature parameters of the gravity field." GEOPHYSICS 81, no. 3 (May 2016): G49—G57. http://dx.doi.org/10.1190/geo2015-0331.1.

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Rotating the gravity gradient tensor about a vertical axis by an appropriate angle allows one to express its components as functions of the curvatures of the equipotential surface. The description permits the identification of the gravity gradient tensor as the Newtonian tidal tensor and part of the tidal potential. The identification improves the understanding and interpretation of gravity gradient data. With the use of the plunge of the eigenvector associated with the largest eigenvalue or plunge of the main tidal force, it is possible to estimate the location and depth of buried gravity sources; this is developed in model data and applied to FALCON airborne gravity gradiometer data from the Canning Basin, Australia.

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23

SASAKURA, NAOKI. "A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY." International Journal of Modern Physics A 25, no. 23 (September 20, 2010): 4475–92. http://dx.doi.org/10.1142/s0217751x10050433.

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Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parametrized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.

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24

Bartolo, Nicola, Luca Caloni, Giorgio Orlando, and Angelo Ricciardone. "Tensor non-Gaussianity in chiral scalar-tensor theories of gravity." Journal of Cosmology and Astroparticle Physics 2021, no. 03 (March 1, 2021): 073. http://dx.doi.org/10.1088/1475-7516/2021/03/073.

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25

ZALALETDINOV, ROUSTAM. "THE AVERAGING PROBLEM IN COSMOLOGY AND MACROSCOPIC GRAVITY." International Journal of Modern Physics A 23, no. 08 (March 30, 2008): 1173–81. http://dx.doi.org/10.1142/s0217751x08040032.

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The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational correlation tensor terms as compared with the Einstein equations of general relativity. This correlation tensor satisfies a system of structure and field equations. An exact cosmological solution to the macroscopic gravity equations for a constant macroscopic gravitational connection correlation tensor for a flat spatially homogeneous, isotropic macroscopic space-time is presented. The correlation tensor term in the macroscopic Einstein equations has been found to take the form of either a negative or positive spatial curvature term. Thus, macroscopic gravity provides a cosmological model for a flat spatially homogeneous, isotropic Universe which obeys the dynamical law for either an open or closed Universe.

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26

DUMITRESCU, Horia, Vladimir CARDOS, and Radu BOGATEANU. "Gravitational waves on Earth and their warming effects." INCAS BULLETIN 13, no. 1 (March 5, 2021): 43–54. http://dx.doi.org/10.13111/2066-8201.2021.13.1.5.

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The gravity or reactive bundle energy is the outlet of the morphogenetic impact, known as “BIG BANG”, creating a bounded ordered/structured universe along with the solar system, including the EARTH-world with its human race. Post-impact, the huge kinetic energy is spread into stellar bodies associated with the light flux under strong mutual connections or gravitational bundle. Einstein’s general relativity theory including the gravitational field can be expressed under a condensed tensor formulation as E  R − Rg =  T where E defines the geometry via a curved space-time structure (R) over the gravity field (1/2Rg), embedded in a matter distribution T The fundamental (ten non-linear partial differential) equations of the gravitational field are a kind of the space-time machine using the curvature of a four-dimensional space-time to engender the gravity field carrying away material structures. Gravity according to the curved space-time theory is not seen as a gravitational force, but it manifests itself in the relativistic form of the space-time curvature needing the constancy of the light speed. But the constant light velocity makes the tidal wave/pulsating energy, a characteristic of solar energy, impossible. The Einstein’s field equation, expressed in terms of tensor formulation along with the constant light speed postulate, needs two special space-time tensors (curvature and torsion) in 4 dimensions, where for the simplicity the torsion/twist tensor is less well approximated (Bianchi identity) leading to a constant/frozen gravity (twist-free gravity).The non-zero torsion tensor plays a significant physical role in the planetary dynamics as a finest gear of a planet, where its spinning rotation is directly connected to the own work and space-time structure (or clock), controlled by light fluctuations (or tidal effect of gravity). The spin correction of Einstein’s gravitational field refers to the curvature-torsion effect coupled with fluctuating light speed. The mutual curvature-torsion bundle self-sustained by the quantum fluctuations of light speed engenders helical gravitational wave fields of a quantum nature where bodies orbit freely in the light speed field (cosmic wind). In contrast to the Einstein’s field equation describing a gravitational frozen field, a quantum tidal gravity model is proposed in the paper.

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27

Vanchurin, Vitaly. "Covariant information theory and emergent gravity." International Journal of Modern Physics A 33, no. 34 (December 10, 2018): 1845019. http://dx.doi.org/10.1142/s0217751x18450197.

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Informational dependence between statistical or quantum subsystems can be described with Fisher information matrix or Fubini-Study metric obtained from variations/shifts of the sample/configuration space coordinates. Using these (noncovariant) objects as macroscopic constraints, we consider statistical ensembles over the space of classical probability distributions (i.e. in statistical space) or quantum wave functions (i.e. in Hilbert space). The ensembles are covariantized using dual field theories with either complex scalar field (identified with complex wave functions) or real scalar field (identified with square roots of probabilities). We construct space–time ensembles for which an approximate Schrodinger dynamics is satisfied by the dual field (which we call infoton due to its informational origin) and argue that a full space–time covariance on the field theory side is dual to local computations on the information theory side. We define a fully covariant information-computation tensor and show that it must satisfy certain conservation equations. Then we switch to a thermodynamic description of the quantum/statistical systems and argue that the (inverse of) space–time metric tensor is a conjugate thermodynamic variable to the ensemble-averaged information-computation tensor. In (local) equilibrium, the entropy production vanishes, and the metric is not dynamical, but away from the equilibrium the entropy production gives rise to an emergent dynamics of the metric. This dynamics can be described approximately by expanding the entropy production into products of generalized forces (derivatives of metric) and conjugate fluxes. Near equilibrium, these fluxes are given by an Onsager tensor contracted with generalized forces and on the grounds of time-reversal symmetry, the Onsager tensor is expected to be symmetric. We show that a particularly simple and highly symmetric form of the Onsager tensor gives rise to the Einstein–Hilbert term. This proves that general relativity is equivalent to a theory of nonequilibrium (thermo)dynamics of the metric, but the theory is expected to break down far away from equilibrium where the symmetries of the Onsager tensor are to be broken.

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28

Crisostomi, Marco, Kazuya Koyama, and Gianmassimo Tasinato. "Extended scalar-tensor theories of gravity." Journal of Cosmology and Astroparticle Physics 2016, no. 04 (April 21, 2016): 044. http://dx.doi.org/10.1088/1475-7516/2016/04/044.

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29

Arbuzov, Andrej, and Boris Latosh. "Effective potential of scalar–tensor gravity." Classical and Quantum Gravity 38, no. 1 (December 10, 2020): 015012. http://dx.doi.org/10.1088/1361-6382/abc572.

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30

Carloni, S., J. A. Leach, S. Capozziello, and P. K. S. Dunsby. "Cosmological dynamics of scalar–tensor gravity." Classical and Quantum Gravity 25, no. 3 (January 22, 2008): 035008. http://dx.doi.org/10.1088/0264-9381/25/3/035008.

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31

SHOJAI, FATIMAH, ALI SHOJAI, and MEHDI GOLSHANI. "SCALAR–TENSOR THEORIES AND QUANTUM GRAVITY." Modern Physics Letters A 13, no. 36 (November 30, 1998): 2915–22. http://dx.doi.org/10.1142/s0217732398003090.

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Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space–time metric. So both gravity and quantum are geometrical features. Gravity determines the causal structure of the space–time, while quantum determines the scale of the space–time. In this letter, it is shown that it is possible to use the scalar-tensor framework to build a unified theory in which both quantum and gravitational effects are present.

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32

Burton, D. A., R. W. Tucker, and C. H. Wang. "Spinning particles in scalar-tensor gravity." Physics Letters A 372, no. 18 (April 2008): 3141–44. http://dx.doi.org/10.1016/j.physleta.2008.01.048.

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33

Berman, Marcelo Samuel. "Lambda-universe in scalar-tensor gravity." Astrophysics and Space Science 323, no. 1 (June 12, 2009): 103–6. http://dx.doi.org/10.1007/s10509-009-0052-4.

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34

Bronnikov, K. A. "Scalar-tensor gravity and conformal continuations." Journal of Mathematical Physics 43, no. 12 (December 2002): 6096–115. http://dx.doi.org/10.1063/1.1519667.

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35

Myung, Yun Soo, and Taeyoon Moon. "Scale-invariant tensor spectrum from conformal gravity." Modern Physics Letters A 30, no. 32 (October 5, 2015): 1550172. http://dx.doi.org/10.1142/s0217732315501722.

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We study cosmological tensor perturbations generated during de Sitter inflation in the conformal gravity with mass parameter [Formula: see text]. It turns out that tensor power spectrum is scale-invariant.

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36

SASAKURA, NAOKI. "TENSOR MODEL FOR GRAVITY AND ORIENTABILITY OF MANIFOLD." Modern Physics Letters A 06, no. 28 (September 14, 1991): 2613–23. http://dx.doi.org/10.1142/s0217732391003055.

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We investigate the relation between rank-three tensor models and the dynamical triangulation model of three-dimensional quantum gravity, and discuss the orientability of the manifold and the corresponding tensor models. We generalize the orientable tensor models to arbitrary dimensions, which include the two-dimensional Hermitian matrix model as a special case.

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37

Obster, Dennis, and Naoki Sasakura. "Counting Tensor Rank Decompositions." Universe 7, no. 8 (August 15, 2021): 302. http://dx.doi.org/10.3390/universe7080302.

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Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how many tensor rank decompositions can approximate a given tensor. More precisely, finding an approximate symmetric tensor rank decomposition of a symmetric tensor Q with an error allowance Δ is to find vectors ϕi satisfying ∥Q−∑i=1Rϕi⊗ϕi⋯⊗ϕi∥2≤Δ. The volume of all such possible ϕi is an interesting quantity which measures the amount of possible decompositions for a tensor Q within an allowance. While it would be difficult to evaluate this quantity for each Q, we find an explicit formula for a similar quantity by integrating over all Q of unit norm. The expression as a function of Δ is given by the product of a hypergeometric function and a power function. By combining new numerical analysis and previous results, we conjecture a formula for the critical rank, yielding an estimate for the spacetime degrees of freedom of the CTM. We also extend the formula to generic decompositions of non-symmetric tensors in order to make our results more broadly applicable. Interestingly, the derivation depends on the existence (convergence) of the partition function of a matrix model which previously appeared in the context of the CTM.

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38

Ichinose, Shoichi. "New Algorithm for Tensor Calculation in Field Theories." International Journal of Modern Physics C 09, no. 02 (March 1998): 243–64. http://dx.doi.org/10.1142/s0129183198000182.

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Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of the graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a special interest. Examples of the leading order calculation of some general invariants such as RμνλσRμνλσ are given. Application to Weyl anomaly calculation is also discussed.

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NAGATA, RYO. "CONSTRAINTS ON SCALAR-TENSOR COSMOLOGY FROM WMAP DATA." International Journal of Modern Physics: Conference Series 01 (January 2011): 183–88. http://dx.doi.org/10.1142/s2010194511000250.

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We place observational constraints on a scalar-tensor gravity theory by comparing the WMAP temperature and polarization angular spectrum with its predictions. We examined the quadratic extension of Brans-Dicke theory and found that, even if the scalar-tensor theory was far from Einstein gravity in early cosmological epochs, CMB can set stringent constraints on the deviations from Einstein gravity.

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Barnes, Gary, and John Lumley. "Processing gravity gradient data." GEOPHYSICS 76, no. 2 (March 2011): I33—I47. http://dx.doi.org/10.1190/1.3548548.

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As the demand for high-resolution gravity gradient data increases and surveys are undertaken over larger areas, new challenges for data processing have emerged. In the case of full-tensor gradiometry, the processor is faced with multiple derivative measurements of the gravity field with useful signal content down to a few hundred meters’ wavelength. Ideally, all measurement data should be processed together in a joint scheme to exploit the fact that all components derive from a common source. We have investigated two methods used in commercial practice to process airborne full-tensor gravity gradient data; the methods result in enhanced, noise-reduced estimates of the tensor. The first is based around Fourier operators that perform integration and differentiation in the spatial frequency domain. By transforming the tensor measurements to a common component, the data can be combined in a way that reduces noise. The second method is based on the equivalent-source technique, where all measurements are inverted into a single density distribution. This technique incorporates a model that accommodates low-order drift in the measurements, thereby making the inversion less susceptible to correlated time-domain noise. A leveling stage is therefore not required in processing. In our work, using data generated from a geologic model along with noise and survey patterns taken from a real survey, we have analyzed the difference between the processed data and the known signal to show that, when considering the Gzz component, the modified equivalent-source processing method can reduce the noise level by a factor of 2.4. The technique has proven useful for processing data from airborne gradiometer surveys over mountainous terrain where the flight lines tend to be flown at vastly differing heights.

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Nekut, A. G. "Borehole gravity gradiometry." GEOPHYSICS 54, no. 2 (February 1989): 225–34. http://dx.doi.org/10.1190/1.1442646.

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Gravity gradients measured in a borehole are of interest due to their direct, simple relation to the density of the formations surrounding the hole. Borehole gravity meters (BHGMs) are used to measure gravity differences along the borehole and from these differences, we compute averaged values for a linear combination of the gravity gradient tensor elements. One way to implement a borehole gravity gradiometer (BHGGM) is to measure the torque exerted on a pair of masses separated by a beam. A BHGGM directly measures all the elements of the gravity gradient tensor. Knowledge of these elements provides information about the direction to density anomalies in the vicinity of the borehole and enhances the analysis of dipping beds. The BHGGM may be superior to the BHGM for resolving the density of thin beds. Density variations remote from the borehole are best detected and characterized by joint interpretation of BHGM and BHGGM data.

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VASSILEVICH, D. V. "QUANTUM GRAVITY ON CP2." International Journal of Modern Physics D 02, no. 02 (June 1993): 135–47. http://dx.doi.org/10.1142/s021827189300012x.

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PADMANABHAN, T. "FROM GRAVITONS TO GRAVITY: MYTHS AND REALITY." International Journal of Modern Physics D 17, no. 03n04 (March 2008): 367–98. http://dx.doi.org/10.1142/s0218271808012085.

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There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full nonlinear Einstein theory of gravity by coupling a massless, spin 2 field hab self-consistently to the total energy–momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein–Hilbert (EH) action; and (iii) it uses only standard concepts in Lorentz-invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect — and critically re-examining several previous attempts — we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is impossible to obtain the EH action, starting from the standard action for gravitons in linear theory and iterating repeatedly. This result follows from the fact that EH action has a part (viz. the surface term arising from second derivatives of the metric tensor) which is nonanalytic in the coupling constant, when expanded in terms of the graviton field. Thus, at best, one can only hope to obtain the remaining, quadratic, part of the EH Lagrangian (viz. the Γ2 Lagrangian) if no additional assumptions are made. Second, we use the Taylor series expansion of the action for Einstein's theory, to identify the tensor [Formula: see text], to which the graviton field hab couples to the lowest order (through a term of the form [Formula: see text] in the Lagrangian). We show that the second rank tensor [Formula: see text] is not the conventional energy–momentum tensor Tab of the graviton and provide an explanation for this feature. Third, we construct the full nonlinear Einstein theory with the source being a spin 0 field, a spin 1 field or relativistic particles by explicitly coupling the spin 2 field to this second rank tensor [Formula: see text] order by order and summing up the infinite series. Finally, we construct the theory obtained by self-consistently coupling hab to the conventional energy–momentum tensor Tab order by order and show that this does not lead to Einstein's theory. The implications are discussed.

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Romeshkani, Mohsen, and Mehdi Eshagh. "DETERMINISTICALLY-MODIFIED INTEGRAL ESTIMATORS OF GRAVITATIONAL TENSOR." Boletim de Ciências Geodésicas 21, no. 1 (March 2015): 189–212. http://dx.doi.org/10.1590/s1982-217020150001000012.

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The Earth's global gravity field modelling is an important subject in Physical Geodesy. For this purpose different satellite gravimetry missions have been designed and launched. Satellite gravity gradiometry (SGG) is a technique to measure the second-order derivatives of the gravity field. The gravity field and steady state ocean circulation explorer (GOCE) is the first satellite mission which uses this technique and is dedicated to recover Earth's gravity models (EGMs) up to medium wavelengths. The existing terrestrial gravimetric data and EGM scan be used for validation of the GOCE data prior to their use. In this research, the tensor of gravitation in the local north-oriented frame is generated using deterministically-modified integral estimators involving terrestrial data and EGMs. The paper presents that the SGG data is assessable with an accuracy of 1-2 mE in Fennoscandia using a modified integral estimatorby the Molodensky method. A degree of modification of 100 and an integration cap size of for integrating terrestrial data are proper parameters for the estimator.

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Doğru, Fikret, and Oya Pamukçu. "Analysis of gravity disturbance for boundary structures in the Aegean Sea and Western Anatolia." Geofizika 36, no. 1 (2019): 53–76. http://dx.doi.org/10.15233/gfz.2019.36.5.

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Western Anatolia has been shaped N–S-trending extensional tectonic regime and W-E trending horst, grabens and active faults due to the collision of Africa, Arabian and Eurasia plates. The borders of the Aegean Sea tectonic is limited between eastern of Greece, western of Anatolia and Hellenic subduction zone in the south of Crete. To evaluate these tectonic elements gravity disturbance data of the Aegean Sea and Western Anatolia was used in this study. It is thought that the gravity disturbance data reflects the tectonic elements and discontinuities way better than gravity anomaly due to the calculation from the difference between gravity and normal gravity at the same point so thus the tensors and invariants of the study area were calculated and the power spectrum method was applied to the gravity disturbance data. Various boundary analysis methods were applied to the gravity disturbance data to compare the discontinuities obtained from the tensors both theoretical and case study. These methods were tested initially on theoretical data. Within the scope of the theoretical study, a single model and three bodies model were taken into consideration. When the results are examined, it is observed that the Tzz tensor component gives very clear information about the location of the structure. Likewise, when the Txx, Tyy components and invariant results are examined, the vertical and horizontal boundaries were successfully obtained. In addition, the mean depths of these structures were determined using the power spectrum method. In the case application stage, the gravity disturbance data obtained from the Earth Gravitational Model of the eastern of the Aegean Sea and western of Anatolia were evaluated. The tensor and invariants of this gravity disturbance data were first calculated. New possible discontinuities have been identified in the tensors and some of the obtained discontinuities were clarified in their previous discussions. Also, the mean depths of the possible structures were calculated by the power spectrum method at four profiles taken from gravity disturbance data. These depth values are consistent with the depth values of the structural discontinuities obtained from previous studies. Finally, the upward continuation was applied to Tyy, Tyz and Tzz tensors up to 20 km. The positive anomaly values in Tyz and Tzz components and negative anomaly values in Tyy component are consistent with the Western Anatolia Transfer Zone. The structural differences between the eastern and the western of Western Anatolia are noteworthy in the upward continued results of the tensors. In addition, the positive and negative anomalies are notable in areas where the big earthquakes occurred in the last 3 years in the Tyz invariants.

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Chakraborty, Sumanta. "Field Equations for Lovelock Gravity: An Alternative Route." Advances in High Energy Physics 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/6509045.

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We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.

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47

张, 晓菲. "Evolution of the Universe in Scalar-Tensor Gravity." Modern Physics 07, no. 06 (2017): 242–48. http://dx.doi.org/10.12677/mp.2017.76028.

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Beiki, Majid. "Analytic signals of gravity gradient tensor and their application to estimate source location." GEOPHYSICS 75, no. 6 (November 2010): I59—I74. http://dx.doi.org/10.1190/1.3493639.

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The analytic signal concept can be applied to gravity gradient tensor data in three dimensions. Within the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector components are Hilbert transform pairs. Three analytic signal functions then are introduced along [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. The amplitude of the first vertical derivative of the analytic signals in [Formula: see text]- and [Formula: see text]-directions enhances the edges of causative bodies. The directional analytic signals are homogenous and satisfy Euler’s homogeneity equation. The application of directional analytic signals to Euler deconvolution on generic models demonstrates their ability to locate causative bodies. One of the advantages of this method is that it allows the automatic identification of the structural index from solving three Euler equations derived from the gravity gradient tensor for a collection of data points in a window. The other advantage is a reduction of interference effects from neighboring sources by differentiation of the directional analytic signals in [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. Application of the method is demonstrated on gravity gradient tensor data in the Vredefort impact structure, South Africa.

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Harikumar, Sreekanth. "Moffat MOdified Gravity (MOG)." Universe 8, no. 5 (April 24, 2022): 259. http://dx.doi.org/10.3390/universe8050259.

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Scalar Tensor Vector Gravity (STVG) or MOdified Gravity (MOG) is a metric theory of gravity with dynamical scalar fields and a massive vector field introduced in addition to the metric tensor. In the weak field approximation, MOG modifies the Newtonian acceleration with a Yukawa-like repulsive term due to a Maxwell–Proca type Lagrangian. This associates matter with a fifth force and a modified equation of motion. MOG has been successful in explaining galaxy rotation curves, cosmological observations and all other solar system observations without the need for dark matter. In this article, we discuss the key concepts of MOG theory. Then, we discuss existing observational bounds on MOG weak field parameters. In particular, we will present our original results obtained from the X-COP sample of galaxy clusters.

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Harikumar, Sreekanth. "Moffat MOdified Gravity (MOG)." Universe 8, no. 5 (April 24, 2022): 259. http://dx.doi.org/10.3390/universe8050259.

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Scalar Tensor Vector Gravity (STVG) or MOdified Gravity (MOG) is a metric theory of gravity with dynamical scalar fields and a massive vector field introduced in addition to the metric tensor. In the weak field approximation, MOG modifies the Newtonian acceleration with a Yukawa-like repulsive term due to a Maxwell–Proca type Lagrangian. This associates matter with a fifth force and a modified equation of motion. MOG has been successful in explaining galaxy rotation curves, cosmological observations and all other solar system observations without the need for dark matter. In this article, we discuss the key concepts of MOG theory. Then, we discuss existing observational bounds on MOG weak field parameters. In particular, we will present our original results obtained from the X-COP sample of galaxy clusters.

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