A class of spherically symmetric solutions to Einstein's equations for a perfect fluid using non-comoving coordinates

Abstract

We give a new class of solutions to Einstein's equations applied to a perfect fluid exhibiting spherical symmetry, using non-comoving coordinates. In general the fluid has expansion, acceleration and shear. A particular case where the parameters can be reduced to one, namely t*, is selected to illustrate properties of the class. This solution has a singularity at the origin r = 0, and a cosmological type singularity at t = t*, but is otherwise well behaved, the fluid pressure p and density μ vanishing as t or r tend to infinity. The null geodesics of the spacetime are calculated, and several associated phenomena are analysed. These include the particle horizon and range of causality, extreme light bending and trapped surfaces.The Raychaudhuri equation for the fluid is used to establish further physical properties. Possible cosmological implications of the model are indicated.