Exact Solutions of a Chaplygin Gas in an Anisotropic Space-Time of Petrov D

Abstract

This document obtains two exact solutions to the anisotropic spacetime of Petrov D by using the model of a perfect fluid. These solutions represent a scenario of a universe in which the pressure P and the energetic density µ of the fluid are inversely proportional (Chaplygin’s type P = −Q2/µ), where Q is a constant of proportionality. It is established that the symmetry of those models, in the proximities when t → 0, is equivalent to the analogues for the dust model, and might tend to behave as the solutions of the flat or vacuum LRS Kasner solution (Local Rotational Symmetry). Although the solutions are not flat or vacuum in any of the cases, in those proximities, the density tends to infinite and with no pressure. When t → ∞, the models tend to behave as the isotropic flat model of the type FRWL. In the analysis of the Hubble and the deceleration parameters obtained that in those solutions, the Hubble’s constant and the deceleration parameter, depend on time and manner in which their values, or tendency, significantly evolve. The deceleration parameter q changes its sign as times passes, so that it represents an initial deceleration process that, in continuity, constantly changes to a process of acceleration.