arXiv subjects

G. G. L. Nashed

Publications and source records attributed to G. G. L. Nashed.

116 records · Page 7Linked to original sources

arXiv2015

Schwarzschild solution in extended teleparallel gravity

Tetrad field, with two unknown functions of radial coordinate and an angle $Φ$ which is the polar angle $ϕ$ times a function of the redial coordinate, is applied to the field equation of modified theory of gravity. Exact vacuum solution is derived whose scalar torsion, $T ={T^α}_{μν} {S_α}^{μν}$, is constant. When the angle $Φ$ coincides with the polar angle $ϕ$, the derived solution will be a solution only for linear form of $f(T)$ gravitational theory.

gr-qc↗

arXiv2014

A Built-in Inflation in the $f(T)$-Cosmology

In the present work we derive an exact solution of an isotropic and homogeneous Universe governed by $f(T)$ gravity. We show how the torsion contribution to the FRW cosmology can provide a \textit{unique} origin for both early and late acceleration phases of the Universe. The three models ($k=0, \pm 1$) show a \textit{built-in} inflationary behavior at some early Universe time; they restore suitable conditions for the hot big bang nucleosynthesis to begin. Unlike the standard cosmology, we show that even if the Universe initially started with positive or negative sectional curvatures, the curvature density parameter enforces evolution to a flat Universe. The solution constrains the torsion scalar $T$ to be a constant function at all time $t$, for the three models. This eliminates the need for the dark energy (DE). Moreover, when the continuity equation is assumed for the torsion fluid, we show that the flat and closed Universe models \textit{violate} the conservation principle, while the open one does not. The evolution of the effective equation of state (EoS) of the torsion fluid implies a peculiar trace from a quintessence-like DE to a phantom-like one crossing a matter and radiation EoS in between; then it asymptotically approaches a de Sitter fate.

gr-qc↗

arXiv2012

On the Regularization of Kerr-NUT spacetime: I

Within the framework of teleparallel equivalent of general relativity (TEGR) theory, calculation of the total energy and momentum of Kerr-NUT spacetimes have been employed using two methods of the gravitational energy-momentum, which is coordinate independent, and the Riemannian connection 1-form, ${\widetildeΓ_α}^β$. It has been shown that the two methods give the same an unacceptable result, i.e., divergent value. Therefore, a local Lorentz transformation that plays a role of a regularizing tool, which subtracts the inertial effects without distorting the true gravitational contribution, has been suggested. This transformation keeps the resulting spacetime to be a solution of the equations of motion of TEGR.

physics.gen-ph↗

arXiv2011

Gravitational radiation fields in teleparallel equivalent of general relativity and their energies

We derive two new retarded solutions in the teleparallel theory equivalent to general relativity (TEGR). One of these solutions gives a divergent energy. Therefore, we used the regularized expression of the gravitational energy-momentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.

gr-qc↗

arXiv2010

Energy of spherically symmetric spacetimes on regularizing teleparallelism

We calculate the total energy of an exact spherically symmetric solutions, i.e., Schwarzschild and Reissner Nordstr$\ddot{o}$m, using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical! Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.

gr-qc↗

arXiv1996

Equivalence principle in the new general relativity

We study the problem of whether the active gravitational mass of an isolated system is equal to the total energy in the tetrad theory of gravitation. The superpotential is derived using the gravitational Lagrangian which is invariant under parity operation, and applied to an exact spherically symmetric solution. Its associated energy is found equal to the gravitational mass. The field equation in vacuum is also solved at far distances under the assumption of spherical symmetry. Using the most general expression for parallel vector fields with spherical symmetry, we find that the equality between the gravitational mass and the energy is always true if the parameters of the theory $a_1$, $a_2$ and $a_3$ satisfy the condition, $(a_1+ a_2) (a_1-4a_3/9)\neq0$. In the two special cases where either $(a_1+a_2)$ or $(a_1-4a_3/9)$ is vanishing, however, this equality is not satisfied for the solutions when some components of the parallel vector fields tend to zero as $1/\sqrt{r}$ for large $r$.

gr-qc↗

arXiv1996

Cosmological Application of the New General Relativity

The field equations of the new general relativity constructed by Hayashi and Shirafuji (1979), have been applied to two different geometric structures, given by Robertson (1932), in the domain of cosmology. In the first application a family of models, involving two of the parameters characterizing the field equations of the new general relativity, is obtained. In the second application the models obtained are found to involve one parameter only. The cosmological parameters in both applications are calculated and some cosmological problems are discussed in comparison with the corresponding results of other field theories.

gr-qc↗

arXiv1996

Energy of General Spherically Symmetric Solution in Tetrad Theory of Gravitation

We find the most general, spherically symmetric solution in a special class of tetrad theory of gravitation. The tetrad gives the Schwarzschild metric. The energy is calculated by the superpotential method and by the Euclidean continuation method. We find that unless the time-space components of the tetrad go to zero faster than ${1/\sqrt{r}}$ at infinity, the two methods give results different from each other, and that these results differ from the gravitational mass of the central gravitating body. This fact implies that the time-space components of the tetrad describing an isolated spherical body must vanish faster than ${1/\sqrt{r}}$ at infinity.

gr-qc↗