Spherically symmetric static space-times and their classification by Ricci inheritance symmetries

Abstract

Ricci inheritance symmetry defines the symmetry directions for the Ricci tensor, as homotheties and conformal Killing vectors are for the metric tensor. Whereas a complete classification of metrics possessing some minimalsymmetry groups exists in the literature for the last two symmetries, no complete listing of space-times metrics and their Ricci inheritance symmetry has been given so far. In this paper we discuss this issue by giving a complete classification of spherically symmetric static space-times by their Ricci inheritance symmetries.