New classes of spherically symmetric, inhomogeneous cosmological models

Abstract

We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe oscillates between two Friedman-Robertson-Walker universes with different spatial curvatures. We show that there exist some spacelike surfaces where the pressure and mass density of the fluid distribution diverge. We study the behavior of our new solutions in their general form as the radial distance goes to zero and infinity. Finally, we briefly address the null geodesics and apparent horizons associated to the obtained solutions. *

FLRW-cosmology in generic gravity theories

“…FLRW metric is mainly used to describe the universe as a homogeneous isotropic fluid distribution [1][2][3][4][5]. For inhomogeneous cosmological solutions, see for example [6][7][8]. On the other hand, current cosmological observations indicate that our universe is undergoing an accelerating expansion phase.…”

D-bound and Bekenstein bound for McVittie solution surrounded by dark energy cosmological fields

“…To clarify more on these features, the McVittie solution has been generalized to the spatially non-flat backgrounds [48]. As the generalizations of the McVittie solution, there are also solutions representing the charged black holes in an expanding FRW universe [49][50][51][52], see also [53] for the general relativistic perfect fluid black hole solutions and [54,55] for the classification and other possible generalizations. In derivation of the general solution in [54] (including the McVittie solution), the scale factor a(t) arises as an integration constant when one integrate the field equations, see Sects.…”

“…In derivation of the general solution in [54] (including the McVittie solution), the scale factor a(t) arises as an integration constant when one integrate the field equations, see Sects. II and III of [54] where q(t) = a(t)/ȧ(t) and the energy-momentum is a perfect fluid. Then, to determine the arbitrary scale factor a(t), one possibility is to consider an equation of state for the matter field supporting the Einstein field equations as it is usually done for the Friedmann equations, i.e p = ωρ, or make an ansatz for its form for various cosmological eras according to the standard model of cosmology.…”

Superposition of FLRW Universes

“…Recently an exact solution of Einstein-perfect fluid system with a spherically symmetric metric in the isotropic coordinates which represents an inhomogeneous cosmological model that allows various interpretations was given in [1]. See [2] and [3,4] for the classification and interpretations of the previously found inhomogeneous cosmological solutions.…”

“…In this work we propose a different interpretation of our solution. The inhomogeneous cosmological model of [1] is a nonlinear superposition of generically two distinct FLRW universes with different spatial curvatures. Nonlinear superposition in general relativity has been studied in the context of Bäcklund transformations [9][10][11][12] for spacetimes that possess two Killing vector fields.…”