scholarly journals Some cosmological solutions of a nonlocal modified gravity

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 619-628 ◽  
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Jelena Grujic ◽  
Zoran Rakic
Keyword(s):  
Gravitational Field ◽  
Modified Gravity ◽  
Riemannian Geometry ◽  
Equations Of Motion ◽  
Nonlocal Term ◽  
Action Functional ◽  
Einstein Theory ◽  
Metric Tensor ◽  
Differentiable Functions ◽  
Cosmological Solutions

We consider nonlocal modification of the Einstein theory of gravity in framework of the pseudo- Riemannian geometry. The nonlocal term has the form H(R)F(?)G(R), where H and G are differentiable functions of the scalar curvature R, and F(?) = ??n=0 fn?n is an analytic function of the d?Alambert operator ?. Using calculus of variations of the action functional, we derived the corresponding equations of motion. The variation of action is induced by variation of the gravitational field, which is the metric tensor g?v. Cosmological solutions are found for the case when the Ricci scalar R is constant.

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 Einstein’s Equation of motion for exterior test particles with spherical mass distribution having varied field, time and radial distance; Golden metric tensors approach.

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Polar Motion ◽  
Equations Of Motion ◽  
Radial Distance ◽  
Equation Of Motion ◽  
Metric Tensor ◽  
Test Particles ◽  
Einstein's Equation ◽  
Spherical Mass ◽  
Metric Tensors

Golden metric tensors exterior to hypothetical distribution of mass whose field varies with time and radial distance have been used to construct the coefficient of affine connections that invariably was used to obtained the Einstein’s equations of motion for test particles of non-zero rest masses. The expression for the variation of time on a clock moving in this gravitational field was derived using the time equation of motion. The test particles in this field under the condition of pure polar motion have an inverse square dependence velocity which depends on radial distance. Our result indicates that despite using the golden metric tensor, the inverse square dependence of the velocity on radial distance has not been changed.

scholarly journals GRAVITATIONAL FIELD OF A GLOBAL MONOPOLE IN A MODIFIED GRAVITY

2011 ◽  
Vol 03 ◽  
pp. 446-454 ◽  
Author(s):  
T. R. P. CARAMÊS ◽  
E. R. BEZERRA DE MELLO ◽  
M. E. X. GUIMARÃES
Keyword(s):  
Gravitational Field ◽  
Modified Gravity ◽  
Field Approximation ◽  
Weak Field ◽  
Symmetric System ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Field Equations ◽  
Metric Tensor

In this paper we analyze the gravitational field of a global monopole in the context of f(R) gravity. More precisely, we show that the field equations obtained are expressed in terms of [Formula: see text]. Since we are dealing with a spherically symmetric system, we assume that F(R) is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.

scholarly journals D = (0|2) DIRAC–MAXWELL–EINSTEIN THEORY AS A WAY FOR DESCRIBING SUPERSYMMETRIC QUARTIONS

1994 ◽  
Vol 09 (09) ◽  
pp. 1555-1568 ◽  
Author(s):  
DMITRIJ P. SOROKIN ◽  
DMITRIJ V. VOLKOV
Keyword(s):  
Gravitational Field ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Dirac Theory ◽  
Einstein Theory ◽  
Abelian Gauge ◽  
Dimensional Space Time

Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin [Formula: see text] and [Formula: see text] (quartions), where the role of quartion momentum in effective (2+1)-dimensional space–time is played by an Abelian gauge superfield propagating in a basic two-dimensional Grassmann-odd space with a cosmological constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd) dimensional model of quartions interacting with the gauge and gravitational field manifests itself as an effective (2 + 1)-dimensional supersymmetric theory.

GRAVITY'S IMMUNITY FROM VACUUM: THE HOLOGRAPHIC STRUCTURE OF SEMICLASSICAL ACTION

2006 ◽  
Vol 15 (12) ◽  
pp. 2303-2308 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Vacuum Energy ◽  
Order Term ◽  
Equations Of Motion ◽  
Vacuum Energy Density ◽  
General Covariance ◽  
Action Functional ◽  
Metric Tensor ◽  
First Order Correction ◽  
Derivatives Of ◽  
Hilbert Action

Principle of equivalence, general covariance and the demand that the variation of the action functional should be well defined lead to a generic Lagrangian for semiclassical gravity of the form L = Qabcd Rabcd with ∇b Qabcd = 0. The expansion of Qabcd in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein–Hilbert action and the first-order correction is given by the Gauss–Bonnet action. Remarkably, any such Lagrangian can be decomposed into surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector and hence gravity does not respond to the changes in the bulk vacuum energy density.

scholarly journals On nonlocal gravity with constant scalar curvature

2018 ◽  
Vol 103 (117) ◽  
pp. 53-59 ◽  
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Zoran Rakic ◽  
Jelena Stankovic
Keyword(s):  
Gravitational Field ◽  
Analytic Function ◽  
Scalar Curvature ◽  
Equations Of Motion ◽  
Constant Scalar Curvature ◽  
Gravity Models ◽  
Nonlocal Term ◽  
Cosmological Scale ◽  
Flrw Universe ◽  
Matter Sector

A class of nonlocal gravity models, where nonlocal term contains an analytic function of the d?Alembert operator _, is considered. For simplicity, these models are considered without matter sector. Related equations of motion for gravitational field g??(x) are presented and analyzed for a constant scalar curvature R. The corresponding solutions for the cosmological scale factor a(t) of the FLRW universe are found and discussed.

scholarly journals A new model of nonlocal modified gravity

2013 ◽  
Vol 94 (108) ◽  
pp. 187-196 ◽  
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Jelena Grujic ◽  
Zoran Rakic
Keyword(s):  
Gravity Model ◽  
Modified Gravity ◽  
Nonlocal Term ◽  
New Model ◽  
Cosmological Solutions

We consider a new modified gravity model with nonlocal term of the form R?1F(?)R. This kind of nonlocality is motivated by investigation of applicability of a few unusual ansatze to obtain some exact cosmological solutions. In particular, we find attractive and useful quadratic ansatz ?R = qR2.

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.

The Permanent Gravitational Field in the Einstein Theory

1920 ◽  
Vol 22 (2) ◽  
pp. 86
Author(s):  
Luther Pfahler Eisenhart
Keyword(s):  
Gravitational Field ◽  
Einstein Theory

scholarly journals The third way to 3D gravity

2015 ◽  
Vol 24 (12) ◽  
pp. 1544015 ◽  
Author(s):  
Eric Bergshoeff ◽  
Wout Merbis ◽  
Alasdair J. Routh ◽  
Paul K. Townsend
Keyword(s):  
Equations Of Motion ◽  
Massive Gravity ◽  
De Sitter ◽  
Gravitational Field Equation ◽  
Third Way ◽  
Metric Tensor ◽  
The Third ◽  
Higher Dimensional ◽  
Conservation Condition ◽  
3D Gravity

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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