Energy and Momentum densities of cosmological models, with equation of state ρ=μ\rho=\mu, in general relativity and teleparallel gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.Comment: 15 pages, no figures, Minor typos corrected; version to appear in International Journal of Theoretical Physic

Energy and Momentum Distributions of Kantowski and Sachs Space-time

We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.Comment: 12 page

Energy and Momentum Densities Associated with Solutions Exhibiting Directional Type Singularities

We obtain the energy and momentum densities of a general static axially symmetric vacuum space-time described by the Weyl metric, using Landau-Lifshitz and Bergmann-Thomson energy-momentum complexes. These two definitions of the energy-momentum complex do not provide the same energy density for the space-time under consideration, while give the same momentum density. We show that, in the case of Curzon metric which is a particular case of the Weyl metric, these two definitions give the same energy only when $R \to \infty$. Furthermore, we compare these results with those obtained using Einstein, Papapetrou and M{\o}ller energy momentum complexes.Comment: 10 pages, references added, minor corrections [Admin note: substantial overlap with gr-qc/0403097 , gr-qc/0403039

Energy Distribution associated with Static Axisymmetric Solutions

This paper has been addressed to a very old but burning problem of energy in General Relativity. We evaluate energy and momentum densities for the static and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen and the gamma metrics, belonging to the Weyl class. We apply four well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and M$\ddot{o}$ller to compute energy-momentum density components. We obtain that these prescriptions do not provide similar energy density, however momentum becomes constant in each case. The results can be matched under particular boundary conditions.Comment: 18 pages, accepted for publication in Astrophysics and SpaceScienc

On the energy of charged black holes in generalized dilaton-axion gravity

In this paper we calculate the energy distribution of some charged black holes in generalized dilaton-axion gravity. The solutions correspond to charged black holes arising in a Kalb-Ramond-dilaton background and some existing non-rotating black hole solutions are recovered in special cases. We focus our study to asymptotically flat and asymptotically non-flat types of solutions and resort for this purpose to the M{\o}ller prescription. Various aspects of energy are also analyzed.Comment: LaTe

Geodesics and Geodesic Deviation in static Charged Black Holes

The radial motion along null geodesics in static charged black hole space-times, in particular, the Reissner-Nordstr\"om and stringy charged black holes are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space-times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space-time. We studied the physical effects of the gravitational field between two test particles in stringy charged black hole and compared the results with that given in Schwarzschild and Reissner-Nordstr\"om black holes.Comment: 12 pages, 5 figures, small changes, figures and references added, conclusions changed. A improved, version accepted in Astrophysics and Space Scienc

The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

According to the Einstein, Weinberg, and M{\o}ller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable nonlinear electrodynamics suggested by Ay\'{o}n-Beato and Garc\'{i}a. The results show that the energy associated with the definitions of Einstein and Weinberg are the same, but M{\o}ller not. Using the power series expansion, we find out that the first two terms in the expression are the same as the energy distributions of the Reissner-Nordstr\"{o}m solution, and the third term could be used to survey the factualness between numerous solutions of the Einstein field eqautions coupled to a nonlinear electrodynamics.Comment: 11 page

Distribution of Energy-Momentum in a Schwarzschild-Quintessence Space-time Geometry

An analysis of the energy-momentum localization for a four-dimensional\break Schwarzschild black hole surrounded by quintessence is presented in order to provide expressions for the distributions of energy and momentum. The calculations are performed by using the Landau-Lifshitz and Weinberg energy-momentum complexes. It is shown that all the momenta vanish, while the expression for the energy depends on the mass $M$ of the black hole, the state parameter $w_{q}$ and the normalization factor $c$. The special case of $w_{q}=-2/3$ is also studied, and two limiting cases are examined.Comment: 9 page

Bergmann-Thomson energy-momentum complex for solutions more general than the Kerr-Schild class

In a very well-known paper, Virbhadra's research group proved that the Weinberg, Papapetrou, Landau and Lifshitz, and Einstein energy-momentum complexes ``coincide'' for all metrics of Kerr-Schild class. A few years later, Virbhadra clarified that this ``coincidence'' in fact holds for metrics more general than the Kerr-Schild class. In the present paper, this study is extended for the Bergmann-Thomson complex and it is proved that this complex also ``coincides'' with those complexes for a more general than the Kerr-Schild class metric.Comment: RevTex, 12 page

The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications

There exist at least a few different kind of averaging of the differences of the energy-momentum and angular momentum in normal coordinates {\bf NC(P)} which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [1-8] giving the {\it canonical superenergy and angular supermomentum tensors}. In this paper we present another averaging of the differences of the energy-momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy-momentum and angular momentum densities. But these averaged relative energy-momentum and angular momentum tensors, closely related to the canonical superenergy and angular supermomentum tensors, {\it depend on some fundamental length $L>0$}. The averaged relative energy-momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to {\it coordinate independent} analysis (local and in special cases also global) of this field. We have applied the averaged relative energy-momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general) universes. The obtained results are very interesting, e.g., the averaged relative energy density is {\it positive definite} for the all Friedman universes.Comment: 30 pages, minor changes referring to Kasner universe