FRW universe models in conformally flat-spacetime coordinates I: General formalism

Abstract

The 3-space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known and also some new transformations to conformally flat spacetime coordinates. A general formula for the recession velocity is deduced.

Stability of generic thin shells in conformally flat spacetimes

“…As of such conformally flat spacetimes one finds the RobertsonWalker cosmological metrics [4][5][6][7], the Einstein-de Sitter spacetime [8] and the Mannheim solution [9]. The LeviCivita-Bertotti-Robinson (LBR) conformally flat solution to the Einstein-Maxwell field equations in the context of general relativity is given by (G = 1 = 4π 0 )…”

“…which was found in [10][11][12][13] and has been interpreted as the spacetime outside a static, massless, charged particle by Lovelock [14,15]. According to Lovelock, in order to avoid the naked singularity, one has to assume that Q < 2r s in which r s stands for the Schwarzschild radius of the particle [14,15].…”

“…According to Lovelock, in order to avoid the naked singularity, one has to assume that Q < 2r s in which r s stands for the Schwarzschild radius of the particle [14,15]. This, however, implies that the singularity cannot be avoided.…”

“…Alternatively, Dolan in [16] has shown that the solution (1) is not spherically symmetric and therefore the physical singularity at r = 0 can be avoided [15]. Recently in [15], by excluding r = 0 from a spherically symmetric a e-mail: zahra.amirabi@emu.edu.tr spacetime, Gron and Johannesen have constructed the LBR spacetime without encountering the physical singularity at r = 0. In this effort they have established a timelike thin shell of radius Q and mass M = Q with flat Minkowski spacetime inside and the LBR solution outside the shell.…”

Spatially open Friedmann–Robertson–Walker Universe fueled with interacting sources

“…Recently, in order to explain the current CMB anisotropy, supernovae and LSS data, and the age of the Universe, the spatially open Friedmann-Robertson-Walker (FRW) spacetime fueled with different types of matter sources has been seen as a possible candidate (Aurich & Steiner 2002;Gron & Johannesen 2011).…”