A class of generalised Robinson-Trautman solutions in non-comoving coordinates

Abstract

A new class of algebraically special solutions is found for Einstein's equations based on the generalised Robinson-Trautman formulation introduced by Wainwright. The solution metrics depend on all four spacetime coordinates t,x,y and r, and in the x,y subspace are either spherically symmetric (parameter K 0 > 0) or spatially flat (K 0 = 0). The inhomogeneous spacetimes, of Petrov type II, have singularities at t = 0 and r = 0. The source is a stiff perfect fluid that expands with shear and acceleration but without rotation. The dynamical configuration in the era t ∼ 0 depends directly on a function h(x,y) of the metric. Trapped surfaces are found, associated with the singularity r = 0, which is shown to be censored.