Post-Newtonian approximation of a new theory of gravity

1981 ◽  
Vol 59 (11) ◽  
pp. 1592-1608 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
Equations Of Motion ◽  
Multipole Expansion ◽  
Momentum Conservation ◽  
Momentum Tensor ◽  
Newtonian Theory ◽  
Perihelion Precession ◽  
Motion Energy ◽  
Newtonian Approximation ◽  
Theory Of Gravity ◽  
Ppn Parameters

The post-Newtonian approximation is developed for a new theory of gravity based on a Hermitian metric gμν. The approximation gives Newtonian theory in lowest order, but differs from general relativity in post-Newtonian order. The equations of motion, energy–momentum conservation, and perihelion precession are investigated. The equations of motion are derivable from the conservation laws of the energy–momentum tensor. A multipole expansion of the metric is formulated, and the PPN parameters α, β, and γ are found all to be unity. Several new parameters occur, most notably I, which is related to the number density of fermions of a system.

A note on a theory of gravity

1977 ◽  
Vol 55 (1) ◽  
pp. 38-42 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Lagrangian Density ◽  
Mathematical Form ◽  
Field Equations ◽  
Newtonian Theory ◽  
Newtonian Approximation ◽  
Theory Of Gravity

An error in a previously published theory of gravity is corrected. Field equations are derived from a Lagrangian density of simple mathematical form. The post-Newtonian approximation is calculated, and the theory is shown to be in agreement with all local observations. The limitations of the standard, parameterized post-Newtonian theory are noted.

scholarly journals Relativistic Effects in Orbital Motion of the S-Stars at the Galactic Center

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 177
Author(s):  
Rustam Gainutdinov ◽  
Yurij Baryshev
Keyword(s):  
Galactic Center ◽  
Strong Field ◽  
Equations Of Motion ◽  
Compact Object ◽  
Relativistic Effects ◽  
Momentum Tensor ◽  
Positive Energy ◽  
Sgr A ◽  
Ppn Parameters ◽  
Very High

The Galactic Center star cluster, known as S-stars, is a perfect source of relativistic phenomena observations. The stars are located in the strong field of relativistic compact object Sgr A* and are moving with very high velocities at pericenters of their orbits. In this work we consider motion of several S-stars by using the Parameterized Post-Newtonian (PPN) formalism of General Relativity (GR) and Post-Newtonian (PN) equations of motion of the Feynman’s quantum-field gravity theory, where the positive energy density of the gravity field can be measured via the relativistic pericenter shift. The PPN parameters β and γ are constrained using the S-stars data. The positive value of the Tg00 component of the gravity energy–momentum tensor is confirmed for condition of S-stars motion.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

UNUSUAL HYDRODYNAMICS

1987 ◽  
Vol 02 (05) ◽  
pp. 1591-1615 ◽  
Author(s):  
V.A. BEREZIN
Keyword(s):  
Black Hole ◽  
Cosmological Model ◽  
Production Process ◽  
Particle Production ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Point Of View ◽  
Modified Equations ◽  
Nonsingular Cosmological Model

A method for the phenomenological description of particle production is proposed. Correspondingly modified equations of motion and energy-momentum tensor are obtained. In order to illustrate this method we reconsider from the new point of view of (i) the C-field Hoyle-Narlikar cosmology, (ii) the influence of the particle production process on metric inside the event horizon of a charged black hole and (iii) a nonsingular cosmological model.

Feldtheoretische Konstruktion der Jordan—Brans—Dicke-Theorie / Fieldtheoretic Construction of the Jordan-Brans-Dicke-Theory

1971 ◽  
Vol 26 (4) ◽  
pp. 599-622
Author(s):  
H. von Grünberg
Keyword(s):  
Gauge Group ◽  
Tensor Field ◽  
Mathematical Proof ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flat Space ◽  
Momentum Tensor ◽  
Field Equations ◽  
Tensor Theory ◽  
Generally Covariant

Abstract In the framework of Lorentz invariant theories of gravitation the fieldtheoretic approach of the generally covariant Jordan-Brans-Dicke-theory is investigated.It is shown that a slight restriction of the gauge group of Einstein's linear tensor theory leads to the linearized Jordan-Brans-Dicke-theory. The problem of the inconsistency of the field equations and the equations of motion is solved by introducing the Landau-Lifschitz energy momentum tensor of the gravitational field as an additional source term into the field equations. The second order of the theory together with the corresponding gauge group are calculated explicitly. By means of the structure of the gauge group of the tensor field it is possible to identify the successive orders of the scalar-tensor theory as an expansion of the Jordan-Brans-Dicke-theory in flat space-time. The question of the uniqueness of the procedure is answered by showing that the structure of the gauge group of the tensor field is predetermined by the linear equations of motion. The mathematical proof of this fact confirms formally the meaning of the equations of motion for the geometry of space.

scholarly journals Rip cosmologies, wormhole solutions and big trip in the f(T,𝒯 ) theory of gravity

2020 ◽  
Vol 17 (08) ◽  
pp. 2050116 ◽  
Author(s):  
Maxime Z. Arouko ◽  
Ines G. Salako ◽  
A. D. Kanfon ◽  
M. J. S. Houndjo ◽  
Etienne Baffou
Keyword(s):  
Energy Momentum Tensor ◽  
Late Phase ◽  
Momentum Tensor ◽  
Cosmological Models ◽  
The Other ◽  
Throat Radius ◽  
Eos Parameter ◽  
Wormhole Throat ◽  
Initial Epoch ◽  
Theory Of Gravity

Rip cosmological models have been investigated in the framework of [Formula: see text] theory of gravity, where [Formula: see text] denotes the torsion and [Formula: see text] is the trace of the energy–momentum tensor. These phantom cosmological models revealed that at initial epoch a EoS parameter [Formula: see text] tends asymptotically at late phase to [Formula: see text] [Formula: see text]. On the other hand, Wormhole Solutions and Big Trip have been subject to an investigation. The wormhole throat radius [Formula: see text] and the conditions to be satisfied to produce the Big Trip phenomenon have been discussed.

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