Exact solutions of plane symmetric cosmological models

Abstract

An exact nonghost solution for a planesymmetric cosmology containing a classical spinor field

Exact solutions admitting isometry groupsGr⫆ AbelianG3

“…As a result of this study there appear metrics [32,36,37] for k 2 =0); (5.3.53) (appears to be a new class up to an arbitrary constant k when ε=1 and reduces to the Tabenski and Taub metric with p=ω (ω<0) [34] for k<0. The other metric from this class gives p=ω with (ω>0) for k>0.…”

“…Evidently the spacetime metric (5.3.29) serves as a source for the vacuum metric (5.3.27). Metric (5.3.29) has been shown to reduce to the perfect fluid metric found by Taub in an implicit form, later found by Hojman and Santamarina, and Collins explicitly [32,36,37] for k 2 =0); (5.3.53) (appears to be a new class up to an arbitrary constant k when ε=1 and reduces to the Tabenski and Taub metric with p=ω (ω<0) [34] for k<0. The other metric from this class gives p=ω with (ω>0) for k>0.…”

“…One may like to probe the conditions given by Hojman and Santamarina and later by Collins [36,37], where the metric (…”

“…with m a constant of integration. Other perfect fluid solutions which admit a maximal G G [36] and later Collins probed further the implicit condition (15.76b) given in [1], of the Taub's metric [32] and were able to find an explicit Type D solution which admits G G 4 3 É as the maximal group, with the equation of state p…”

Static plane symmetric relativistic fluids and empty repelling singular boundaries

“…The aim of this paper is to show that the solution found by Collins [5] for a static and plane symmetric relativistic perfect fluid obeying an equation of state such that ρ and p are proportional to each other (see also [6] and for the case ρ = p [7]) exhibits such a property.…”