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.

scholarly journals ENERGY–MOMENTUM IN VISCOUS KASNER-TYPE UNIVERSE IN BERGMANN–THOMSON FORMULATIONS

2005 ◽  
Vol 20 (10) ◽  
pp. 2169-2177 ◽  
Author(s):  
MUSTAFA SALTI ◽  
ALI HAVARE
Keyword(s):  
Total Energy ◽  
Space Time ◽  
Cosmological Models ◽  
Energy And Momentum ◽  
Momentum Complex ◽  
The Universe ◽  
Friedmann Robertson Walker

Using the Bergmann–Thomson energy–momentum complex and its tele-parallel gravity version, we obtain the energy and momentum of the universe in viscous Kasner-type cosmological models. The energy and momentum components (due to matter plus field) are found to be zero and this agree with a previous work of Rosen and Johri et al. who investigated the problem of the energy in Friedmann–Robertson–Walker universe. The result that the total energy and momentum components of the universe in these models is zero supports the viewpoint of Tryon. Rosen found that the energy of the Friedmann–Robertson–Walker space–time is zero, which agrees with the studies of Tryon.

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 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.

scholarly journals What are the wild waves saying? Yet another meditation on the predictions, searches for, and detections of gravitational waves

2018 ◽  
Vol 27 (14) ◽  
pp. 1830009
Author(s):  
Virginia Trimble
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Point Of View ◽  
Large Majority ◽  
Laboratory Apparatus ◽  
New Information ◽  
Theory Of Gravity ◽  
To Come ◽  
The Universe

A large majority of the physics and astronomy communities are now sure that gravitational waves exist, can be looked for, and can be studied via their effects on laboratory apparatus as well as on astronomical objects. So far, everything found out has agreed with the predictions of general relativity, but hopes are high for new information about the universe and its contents and perhaps for hints of a better theory of gravity than general relativity (which even Einstein expected to come eventually). This is one version of the story, from 1905 to the present, told from an unusual point of view, because the author was, for 28.5 years, married to Joseph Weber, who built the first detectors starting in the early 1960s and operated one or more until his death on 30 September 2000.

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 Asymptotically flat vacuum solution in modified theory of Einstein’s gravity

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Surajit Kalita ◽  
Banibrata Mukhopadhyay
Keyword(s):  
General Relativity ◽  
Vacuum Solution ◽  
Compact Objects ◽  
Schwarzschild Solution ◽  
Asymptotically Flat ◽  
Symmetric Vacuum ◽  
Theory Of Gravity ◽  
Bound Orbits ◽  
Vacuum Spacetime ◽  
The Universe

Abstract A number of recent observations have suggested that the Einstein’s theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to surpass the general relativity which explains a number of phenomena where Einstein’s theory of gravity fails. In the f(R) gravity, behaviour of the spacetime is modified as compared to that of given by the Einstein’s theory of general relativity. This theory has already been explored for understanding various compact objects such as neutron stars, white dwarfs etc. and also describing evolution of the universe. Although researchers have already found the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that the metric does have some diverging terms and hence these solutions are not asymptotically flat. We show that it is possible to have asymptotically flat spherically symmetric vacuum solution for the f(R) gravity, which is different from the Schwarzschild solution. We use this solution for explaining various bound orbits around the black hole and eventually, as an immediate application, in the spherical accretion flow around it.

Orbits

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Milky Way ◽  
Extrasolar Planets ◽  
Binary Star ◽  
Milky Way Galaxy ◽  
Newtonian Model ◽  
Theory Of Gravity ◽  
The Masses ◽  
The Universe

Orbits are ubiquitous in the universe: moons orbit planets, planets orbit stars, stars orbit around the center of the Milky Way galaxy, and so on. Any theory of gravity will have to explain the properties of all these orbits. To pave the way for developing the metric theory of gravity (general relativity) this chapter examines the basics of orbits as observed and as explained by the Newtonian model of gravity. We can use our understanding of gravity to infer the masses and other properties of these cosmic systems. Te chapter concludes with four optional sections in this spirit, covering the slingshot maneuver; dark matter; binary star orbits and how they reveal the masses of stars; and extrasolar planets.

Energy and momentum in general relativity. II. The total energy and momentum of an isolated axi-symmetric system generating gravitational waves

1964 ◽  
Vol 282 (1390) ◽  
pp. 372-379 ◽  
Keyword(s):  
General Relativity ◽  
Total Energy ◽  
Gravitational Waves ◽  
Preceding Paper ◽  
Symmetric System ◽  
Uniform Motion ◽  
Field Equations ◽  
Invariant Integrals ◽  
Definition Of ◽  
Energy And Momentum

In the preceding paper the author has developed a theory in which the components of the total 4-momentum of a system are given in terms of four invariant integrals. The theory is applied to the axi-symmetric solution of the general relativity field equations for an isolated system generating gravitational waves obtained by Bondi, van der Burg & Metzner. It is shown that the total energy of the system agrees exactly with the definition of mass adopted by these authors. An expression is obtained for the total momentum along the axis of symmetry. A Schwarzschild system in uniform motion is considered as an example of non-radiative motion.

Inhomogeneous solutions in cosmology

1990 ◽  
Vol 68 (9) ◽  
pp. 824-826
Author(s):  
Paul S. Wesson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Particle Physics ◽  
Quantum Field ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Cosmological Solutions ◽  
The Universe ◽  
Friedmann Robertson Walker

The standard cosmological solutions of Einstein's equations of general relativity describe a fluid that is homogeneous and isotropic in density and pressure. These solutions, often called the Friedmann–Robertson–Walker solutions, are believed to be good descriptions of the universe at the present time. But early on, processes connected with particle physics and quantum field theory may have caused localized inhomogeneities, and recently some new kinds of solution of Einstein's equations have been found, which may describe such regions. In one solution being studied by Wesson and Ponce de Leon (Phys. Rev. D: Part. Fields, 39, 420 (1989)), the density is still uniform but the pressure is nonuniform about a centre. The mass is given by a relation that looks like the familiar Newtonian relation m = (4/3)πR3ρ. However, the solution has other properties that are quite strange (e.g. a region of negative pressure and a kind of dipolar geometry). It is not known if solutions like this are merely mathematical curiosities or imply something about the behaviour of real matter in extreme situations.

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