In this paper we have examined the validity of a proposed definition of gravitational entropy in the context of accelerating black hole solutions of the Einstein field equations, which represent the realistic black hole solutions. We have adopted a phenomenological approach proposed in [20] and expanded in [21], in which the Weyl curvature hypothesis is tested against the expressions for the gravitational entropy. Considering the C-metric for the accelerating black holes, we have evaluated the gravitational entropy and the corresponding entropy density for four different types of black holes, namely, non-rotating black hole, non-rotating charged black hole, rotating black hole and rotating charged black hole. We end up by discussing the merits of such an analysis and the possible reason of failure in the particular case of rotating charged black hole and comment on the possible resolution of the problem.

In this paper, we have studied the propagation of axial gravitational waves in Bianchi I universe using the Regge–Wheeler gauge. In this gauge, there are only two nonzero components of [Formula: see text] in the case of axial waves: [Formula: see text] and [Formula: see text]. The field equations in absence of matter have been derived both for the unperturbed as well as axially perturbed metric. These field equations are solved simultaneously by assuming the expansion scalar [Formula: see text] to be proportional to the shear scalar [Formula: see text] (so that [Formula: see text], where [Formula: see text], [Formula: see text] are the metric coefficients and [Formula: see text] is an arbitrary constant), and the wave equation for the perturbation parameter [Formula: see text] has been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined [Formula: see text]. We then discuss a few special cases to interpret the results. We find that the anisotropy of the background spacetime is responsible for the damping of the gravitational waves as they propagate through this spacetime. The perturbations depend on the values of the angular momentum [Formula: see text]. The field equations in the presence of matter reveal that the axially perturbed spacetime leads to perturbations only in the azimuthal velocity of the fluid leaving the matter field undisturbed.

In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe and leads to a geometric interpretation of dynamical dark energy. The five-dimensional field equations are constructed and its solutions are obtained. The nature of modifications produced by this warp factor in the bulk geometry is discussed. The hypersurface is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the effective cosmological constant of the four-dimensional universe is a variable quantity monitored by the time-dependent warp factor. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times.

We have studied the dynamics of a cylindrical column of anisotropic, charged fluid which is experiencing dissipation in the form of heat flow, free-streaming radiation, and shearing viscosity, undergoing gravitational collapse. We calculate the Einstein-Maxwell field equations and, using the Darmois junction conditions, match the interior non-static cylindrically symmetric space-time with the exterior anisotropic, charged, cylindrically symmetric space-time. The behavior of the density, pressure and luminosity of the collapsing matter has been analyzed. From the dynamical equations, the effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we have derived the solutions for the collapsing matter which is valid during the later stages of collapse and have discussed the significance from a physical standpoint.Comment: 13 pages, 3 figures, submitted. Minor change in the introductio

In this paper we study the evolution of the FRW universe filled with variable modified Chaplygin gas (VMCG). We begin with a thermodynamical treatment of VMCG described by the equation of state P = Aρ − Bρ −α , and obtain its temperature as a function of redshift z. We show that the results are consistent with similar works on other types of Chaplygin gas models. In addition to deriving the exact expression of temperature of the fluid in terms of the boundary conditions and redshift, we also used observational data to determine the redshift at the epoch of transition from the decelerated to the accelerated phase of expansion of the universe. The values of other relevant parameters like the Hubble parameter, the equation-of-state parameter and the speed of sound are obtained in terms of the redshift parameter, and these values are compared with the results obtained from previous works on MCG and other Chaplygin gas models for the various values of n permitted by thermodynamic stability. We assume the present value of temperature of the microwave background radiation to be given by T 0 = 2.7K, and the parameter A in the equation of state is taken as 1/3 since it corresponds to the radiation-dominated phase of the universe. The value of the parameter Ω x has been assumed to be 0.7 in our calculation. Since it is known that the redshift of photon decoupling is z 1100, we used this value to calculate the temperature of decoupling.