scholarly journals A Note on Lagrangians and Lovelock-Rund’s Identities

2015 ◽  
Vol 20 (2) ◽  
pp. 136-139
Author(s):  
Gyan Bahadur Thapa ◽  
J. López Bonilla
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Conservation Laws ◽  
Science And Technology ◽  
Continuity Equations ◽  
Theory Of Gravity ◽  
Energy And Momentum

Lagrangians and Lovelock-Rund’s identities are important derivations in theory of gravity which is generalization of Einstein's theory of general relativity. In this paper, we construct continuity equations in arbitrary Riemannian 4- spaces, which could be interpreted as conservation laws for the energy and momentum of the gravitational field. We put special attention in general relativity.Journal of Institute of Science and Technology, 2015, 20(2): 136-139

scholarly journals DIFFERENT APPROACHES FOR MØLLER'S ENERGY IN THE KASNER-TYPE SPACETIME

2005 ◽  
Vol 20 (28) ◽  
pp. 2175-2182 ◽  
Author(s):  
MUSTAFA SALTI
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Energy Distribution ◽  
Total Energy ◽  
Theory Of Gravity ◽  
Energy And Momentum ◽  
The Universe ◽  
Friedmann Robertson Walker

Considering the Møller energy definition in both Einstein's theory of general relativity and tele-parallel theory of gravity, we find the energy of the universe based on viscous Kasner-type metrics. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories and this result agrees with previous works of Cooperstock and Israelit et al., Banerjee–Sen, Vargas who investigated the problem of the energy in Friedmann–Robertson–Walker universe in Einstein's theory of general relativity and Aydogdu–Saltı who considered the same problem in tele-parallel gravity. In all of these works, they found that the energy of the Friedmann–Robertson–Walker spacetime is zero. Our result is the same as that obtained in the studies of Saltı and Havare. They used the viscous Kasner-type metric and found the total energy and momentum by using Bergmann–Thomson energy–momentum formulation in both general relativity and tele-parallel gravity. The result that the total energy and momentum components of the universe is zero supports the viewpoints of Albrow and Tryon.

scholarly journals Foundations of a Theory of Gravity with a Constraint and Its Canonical Quantization

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Alexander P. Sobolev
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Early Universe ◽  
Canonical Quantization ◽  
Entropy Density ◽  
Maximum Temperature ◽  
Past Century ◽  
Physical Point ◽  
Theory Of Gravity ◽  
The Universe

AbstractThe gravitational equations were derived in general relativity (GR) using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity (GR) and the unimodular theory of gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random.

SPACE–TIME ENERGY–MOMENTUM, THE OBSERVER AND UNCERTAINTY IN GENERAL RELATIVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2353-2359 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
M. J. DUPRE
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Uncertainty Principle ◽  
Ricci Tensor ◽  
Space Time ◽  
Energy Integral ◽  
New Approach ◽  
Extended Space ◽  
Energy And Momentum

In this essay, we introduce a new approach to energy–momentum in general relativity. Space–time, as opposed to space, is recognized as the necessary arena for its examination, leading us to define new extended space–time energy and momentum constructs. From local and global considerations, we conclude that the Ricci tensor is the required element for a localized expression of energy–momentum to include the gravitational field. We present and rationalize a fully invariant extended expression for space–time energy, guided by Tolman's well-known energy integral for an arbitrary bounded stationary system. This raises fundamental issues which we discuss. The role of the observer emerges naturally and we are led to an extension of the uncertainty principle to general relativity, of particular relevance to ultra-strong gravity.

scholarly journals Kerr-Taub-NUT General Frame, Energy, and Momentum in Teleparallel Equivalent of General Relativity

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Field ◽  
Total Energy ◽  
Kerr Black Hole ◽  
Gravitational Energy ◽  
Axially Symmetric ◽  
Riemannian Connection ◽  
Energy And Momentum

A new exact solution describing a general stationary and axisymmetric object of the gravitational field in the framework of teleparallel equivalent of general relativity (TEGR) is derived. The solution is characterized by three parameters “the gravitational massM, the rotationa, and the NUTL.” The vierbein field is axially symmetric, and the associated metric gives the Kerr-Taub-NUT spacetime. Calculation of the total energy using two different methods, the gravitational energy momentum and the Riemannian connection 1-formΓα̃β, is carried out. It is shown that the two methods give the same results of energy and momentum. The value of energy is shown to depend on the massMand the NUT parameterL. IfLis vanishing, then the total energy reduced to the energy of Kerr black hole.

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.

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

scholarly journals Conservation Laws for Collisions of Branes and Shells in General Relativity

2002 ◽  
Vol 88 (18) ◽  
Author(s):  
David Langlois ◽  
Kei-ichi Maeda ◽  
David Wands
Keyword(s):  
General Relativity ◽  
Conservation Laws
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