arXiv subjects
Publications and source records attributed to Farook Rahaman.
Two variable $Λ$ models, viz. $Λ\sim (\dot a/a)^2$ and $Λ\sim ρ$ have been studied under the assumption that the equation of state parameter $ω$ is a function of time. The selected $Λ$ models are found to be equivalent both in four and five dimensions. The possibility of signature flip of the deceleration parameter is also shown.
We here investigate a cosmological model in which three fluids interact with each other involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling `triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under triple interacting fluids will cross the phantom divide.
We investigate the spacetime of anisotropic stars admitting conformal motion. The Einstein field equations are solved using different ansatz of the surface tension. In this investigation, we study two cases in details with the anisotropy as: [1] $p_t = n p_r$ [2] $p_t - p_r = \frac{1}{8 π}(\frac{c_1}{r^2} + c_2)$ where, n, $c_1$ and $c_2$ are arbitrary constants. The solutions yield expressions of the physical quantities like pressure gradients and the mass.
In this paper, we have presented an algorithm to generate various black hole solutions in general relativity and alternative theories of gravity. The algorithm involves few dimensional parameters that are assigned suitable values to specify the required black hole.
Exact solutions of the Einstein field equations with cosmic string and space varying cosmological constant, viz., $Λ= Λ(r)$, in the energy-momentum tensors are presented. Three cases have been studied: where variable cosmological constant (1) has power law dependence, (2) is proportional to the string fluid density, and (3) is purely a constant. Some cases of interesting physical consequences have been found out such that (i) variable cosmological constant can be represented by a power law of the type $Λ=3r^{-2}$, (ii) variable cosmological constant and cosmic string density are interdependent to each other according to the relation $Λ=-8πρ_s$, and (iii) cosmic string density can be scaled by a power law of the type $ρ_s=r^{-2}$. It is also shown that several known solutions can be recovered from the general form of the solutions obtained here.
The standard model of cosmology is investigated using time dependent cosmological constant $Λ$ and Newton's gravitational constant $G$. The total energy content is described by the modified Chaplygin gas equation of state. It is found that the time dependent constants coupled with the modified Chaplygin gas interpolate between the earlier matter to the later dark energy dominated phase of the universe. We also achieve a convergence of parameter $ω\to-1$, with minute fluctuations, showing an evolving $ω$. Thus our model fairly alleviates the cosmic coincidence problem which demands $ω=-1$ at present time.
In this article, Einstein-Maxwell space-time has been considered in connection to some of the astrophysical solutions as previously obtained by Tolman (1939) and Bayin (1978). The effect of inclusion of charge into these solutions has been investigated thoroughly and also the nature of fluid pressure and mass density throughout the sphere have been discussed. Mass-radius and mass-charge relations have been derived for various cases of the charged matter distribution. Two cases are obtained where perfect fluid with positive pressures give rise to electromagnetic mass models such that gravitational mass is of purely electromagnetic origin.
The gravitational field of both local and global non static cosmic strings in the context of Lyra geometry are investigated. Local strings are characterized by having an energy momentum tensor whose only non null components are $T_{tt} = T_{zz}$ . As linearized Einstein equations are formally analogous to the Maxwell equations, the exterior solution does not depend on the radial distribution of the source and hence a Dirac d function was used to approximate the radial distribution of the energy momentum tensor for a local cosmic string along the z-axis: $T_{ab} = δ(x) δ(y)diag (σ, 0, 0, σ) $, $σ$being the energy density of the string [A.Vilenkin. Phys.Rep.(1985)121,263]. For a global string, the energy momentum tensor components are calculated from the action density for a complex scalar field y along with a Maxican hat potential. The gravitational field of the global string is shown to be attractive in nature.
In this paper, we consider global texture with time dependent displacement vector based on Lyra geometry in normal gauge i.e. displacement vector ϕ_i^* = (β_0(t),0,0,0). We investigate gravitational field of global texture configuration by solving Einstein equations as well as that for the scalar field due to texture.