Mustafa Salti

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

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.

Relative Energy-Momentum of the Bianchi-I Type Universes in Teleparallel Gravity

This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0011027, gr-qc/0205028, and gr-qc/0303034.Using the teleparallel gravity versions of the Einstein and Landau–Lifshitz’s energy and/or momentum complexes, I 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 (FRW) universe. The result that the total energy and momentum components of the universe in these models is zero same as Bergmann–Thomson’s energy–momentum and props the viewpoint of Tryon. Rosen found that the energy of the FRW space–time is zero, which agrees with the studies of Tryon.

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

Considering the Moller energy definition in both Einsteins 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 Einsteins theory of general relativity and Aydogdu–Salti 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 Salti 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.

Energy Density Associated with the Bianchi Type-II Space-Time

To calculate the total energy distribution (due to both matter and fields including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type-II space-times. We use the Bergmann-Thomson energy-momentum complex in both general relativity and teleparallel gravity. We find that the energy density in these different gravitation theories is vanishing at all times. This result is the same as that obtained by one of the present authors who solved the problem of finding the energy-momentum in LRS Bianchi type-II by using the energy-momentum complexes of Einstein and Landau and Lifshitz. The results of this paper also are consistent with those given in the previous works of Cooperstock and Israelit,

On the energy-momentum in closed universes

Using the Moller, Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum definitions both in general relativity and teleparallel gravity, we find the energy-momentum of the closed universe based on the generalized Bianchi-I type metric.

Energy in the Schwarzschild-de Sitter Spacetime

The energy (due to matter and fields including gravitation) of the Schwarzschild-de Sitter spacetime is investigated by using the Møller energy-momentum definition in both general relativity and teleparallel gravity. We found the same energy distribution for a given metric in both of these different gravitation theories. It is also independent of the teleparallel dimensionless coupling constant, which means that it is valid in any teleparallel model. Our results sustain that (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerfifi concept of energy and momentum.

The momentum 4-vector in bulk viscous Bianchi type-V space-time

Using the Einstein and Bergmann-Thomson prescriptions, the energy and momentum distributions for the Bianchi type-V bulk viscous space-time are evaluated in both general relativity and the teleparallel gravity (the tetrad theory of gravity). It is shown that for the Bianchi type-V bulk viscous solution, the energy and momentum due to matter and fields including gravity are the same in both the methods used. This paper indicates an important point that these energy-momentum definitions agree with each other not only in general relativity but also in teleparallel gravity and sustains the results obtained by some physicist who show that the energy-momentum definitions of Einstein, Landau-Lifshitz, Papapetrou, Weinberg, Penrose and Bergmann-Thomson complexes give the same energy expression in general relativity.

Extended scalar–tensor theory and thermodynamics in teleparallel framework

We present here a new modified gravitation theory for the galactic dark energy effect by using a general Lagrangian density which is represented by an arbitrary function f(T, ϕ, X) where T describes the torsion scalar in teleparallel gravity while X shows the kinetic scalar field energy. While the function is in general form, once reduced, the model can be transformed into some of the other well-known gravitation theories. After deriving the corresponding field equations and considering the flat Friedmann–Robertson–Walker type universe which is filled with ordinary cosmic matter, we discuss both the non-equilibrium and equilibrium profiles of galactic thermodynamics. We find that there exists an equilibrium picture of thermodynamics. Additionally, we also generalize ordinary f(T, ϕ, X) model’s action to the case in which there exists an interaction between the chameleon and scalar fields.

KALUZA-KLEIN NATURE OF ENTROPY FUNCTION

In the present study, we mainly investigate the nature of entropy function in non-flat Kaluza–Klein universe. We prove that the first and generalized second laws of gravitational thermodynamics are valid on the dynamical apparent horizon.

Energy of a Charged Wormhole

The Møller energy(due to matter and fields including gravity) distribution of the traversable Lorentzian wormhole space-time by the scalar field or electric charged is studied in two different approaches of gravity such as general relativity and tele-parallel gravity. The results are found exactly the same in these different approximations. The energy found in tele-parallel gravity is also independent of the tele-parallel dimensionless coupling constant, which means that it is valid in any tele-parallel model. Our results sustains that (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given space-time and (b) the viewpoint of Lassner that the Møller energy-momentum complex is a powerful concept of energy and momentum.