Energy-Momentum of a Stationary Beam of Light in Teleparallel Gravity

In this paper, we utilize the teleparallel gravity analogs of the energy and momentum definitions of Bergmann-Thomson and Landau-Lifshitz in order to explicitly evaluate the energy distribution (due to matter and fields including gravity) based on the Bonnor space-time, it is shown that for a stationary beam of light, these energy-momentum definitions give the same result. Furthermore, this result supports the viewpoint of Cooperstock and also agree with the previous works by Bringley and Gad.     

Energy of a Stringy Charged Black Hole in the Teleparallel Gravity

We use the teleparallel geometry analog of the Møller energy-momentum complex to calculate the energy distribution (due to matter plus field including gravity) of a charged black hole solution in heterotic string theory. We find the same energy distribution as obtained by Gad who investigated the same problem by using the Møller energy-momentum complex in general relativity. The total energy depends on the black hole mass M and charge Q. The energy obtained is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. Furthermore, our results also sustains (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 powerful concept of energy and momentum.     

Tachyonic teleparallel dark energy

Teleparallel gravity is an equivalent formulation of general relativity in which instead of the Ricci scalar R, one uses the torsion scalar T for the Lagrangian density. Recently teleparallel dark energy has been proposed by Geng et al. (in Phys. Lett. B 704, 384, 2011). They have added quintessence scalar field, allowing also a non-minimal coupling with gravity in the Lagrangian of teleparallel gravity and found that such a non-minimally coupled quintessence theory has a richer structure than the same one in the frame work of general relativity. In the present work we are interested in tachyonic teleparallel dark energy in which scalar field is responsible for dark energy in the frame work of torsion gravity. We find that such a non-minimally coupled tachyon gravity can realize the crossing of the phantom divide line for the effective equation of state. Using the numerical calculations we display such a behavior of the model explicitly.     

Schwarzschild black hole in dark energy background

In this paper we present an exact solution of Einstein’s field equations describing the Schwarzschild black hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black hole is embedded into the dark energy space producing Schwarzschild-dark energy black hole. It is found that the space-time geometry of Schwarzschild-dark energy solution is non-vacuum Petrov type D in the classification of space-times. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor of the Schwarzschild-dark energy solution. We also find that the energy-momentum tensor of the Schwarzschild-dark energy solution violates the strong energy condition due to the negative pressure leading to a repulsive gravitational force of the matter field in the space-time. It is shown that the time-like vector field for an observer in the Schwarzschild-dark energy space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity and the area of the horizons for the Schwarzschild-dark energy black hole.     

Dark energy as space-time curvature induced by quantum vacuum fluctuations

It is shown that quantum vacuum fluctuations give rise to a curvature of space-time equivalent to a cosmological constant, that is a homogeneous energy density ρ and pressure p fulfilling −p=ρ>0. The fact that the fluctuations produce curvature, even if the vacuum expectation of the energy vanishes, is a consequence of the non-linear character of the Einstein equation. A calculation is made, involving plausible hypotheses within quantized gravity, which establishes a relation between the two-point correlation of the vacuum fluctuations and the space-time curvature. Arguments are given which suggest that the density ρ might be of order the “dark energy” density currently assumed to explain the observed accelerated expansion of the universe.     

Holographic dark energy with time depend gravitational constant in the non-flat Ho?ava-Lifshitz cosmology

We study the holographic dark energy on the subject of Hořava-Lifshitz gravity with a time dependent gravitational constant G(t), in the non-flat space-time. We obtain the differential equation that specify the evolution of the dark energy density parameter based on varying gravitational constant. We find out a relation for the state parameter of the dark energy equation of state to low red-shifts which containing varying G corrections in the non-flat space-time.     

Energy–Momentum In The Viscous Kasner-Type Universe In Teleparallel Gravity

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. PACs Numbers: 04.20.-q; 04.50.+h An erratum to this article is available at .     

Energy distribution of a stationary beam of light

Aguirregabiria et al. showed that Einstein, Landau and Lifshitz, Papapetrou, and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric. Bringely used their general expression of the Kerr-Schild class and found energy and momentum densities for the Bonnor metric. In this paper the latter results are obtained without using Aguirregabiria et al results. This also supports Aguirregabiria et al results as well as Cooperstock hypothesis. We obtain further the energy distribution of the space-time under consideration.     

Self-gravitating fluid in a conformally-flat space-time

The Einstein field equations for an irrotational perfect fluid with pressurep, equal to energy density are studied when the space-time is conformally flat. The coordinate transformation to co-moving coordinates is discussed. The energy and Hawking-Penrose inequalities are studied. Static and non-static solutions of the field equations are obtained. It is interesting to note that in the static case the only spherically-symmetric conformally flat solution for self-gravitating fluid is simply the empty flat space-time of general relativity.     

Gravitational energy, momentum and angular momentum of Schwarzschild Anti-de Sitter space-times in the teleparallel equivalent of general relativity

We give a class of spherically symmetric-Anti de Sitter (Ads), exact solution in the teleparallel equivalent of general relativity (TEGR). The solution depends on an arbitrary function F(R)\mathcal{F}(R) and reproduce the metric of Schwarzschild Ads space-time. In the context of the Hamiltonian formulation of the TEGR we compute the gravitational energy of this class. The calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. We show that the form of the energy depends on the arbitrary function. We make a constrain on this arbitrary function to give the correct form of energy.     

Cosmology of f(T) gravity in a holographic dark energy and nonisotropic background

It is shown that the acceleration of the universe can be understood by considering a f(T) gravity models. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. For these f(T) gravity models, a variant of the accelerating cosmology reconstruction program is developed. We consider spatially homogenous and anisotropic Bianchi type I universe in the context of f(T) gravity. The de Sitter, power-law and general exponential solutions are assumed for the scale factor in each spatial direction and the corresponding cosmological models are reconstructed. We reconstruct f(T) theories from two different holographic dark energy models in different time durations. For the holographic dark energy model, the dark energy dominated era with new setting up is chosen for reconstruction, and the Ricci dark energy model, radiation, matter and dark energy dominated time durations are all investigated. Finally we have obtained a modified gravity action consistent with the holographic dark energy scenario.     

Non-vacuum static cylindrically symmetric solution and energy distribution in f(R) gravity

In this paper, we investigate static cylindrically symmetric solution in metric f(R) gravity by taking matter in the form of dust. The assumption of constant Ricci scalar curvature is taken to find the solution. The energy distribution of this solution is explored by applying Landau-Lifshitz energy-momentum complex. In addition, we explore the stability as well as constant scalar curvature conditions for some viable f(R) models along with their energy distribution. It is interesting to mention here that these models satisfy the above mentioned conditions.     

Relativistic parametric embedding class I solutions of cold stars in Karmarkar space-time continuum

The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency.     

Vaidya black hole in non-stationary de Sitter space: Hawking’s temperature

In this paper we present a class of non-stationary solutions of Einstein’s field equations describing embedded Vaidya-de Sitter black holes with a cosmological variable function Λ(u). The Vaidya-de Sitter black hole is interpreted as the radiating Vaidya black hole is embedded into the non-stationary de Sitter space with variable Λ(u). The energy-momentum tensor of the Vaidya-de Sitter black hole is expressed as the sum of the energy-momentum tensors of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor. We find the violation of the strong energy condition due to the negative pressure and leading to a repulsive gravitational force of the matter field associated with Λ(u) in the space-time. We also find that the time-like vector field for an observer in the Vaidya-de Sitter space is expanding, accelerating, shearing and non-rotating. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is Petrov type D in the classification of space-times. We also find the Vaidya-de Sitter black hole radiating with a thermal temperature proportional to the surface gravity and entropy also proportional to the area of the cosmological black hole horizon.     

Dust acoustic localized structures in an electron depleted dusty plasma with two-suprathermal ion-temperature

We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We introduce a class of solutions in which an accelerating expansion is possible in a spatially flat universe for positive and large values of the Brans-Dicke parameter consistent with local gravity experiments. In this Einstein frame formulation, the theory appears as an interacting quintessence model in which the interaction term is given by the conformal transformation. In such an interacting model, we shall show that the solutions lead simultaneously to a constant ratio of energy densities of matter and the scalar field.