On Ricci inheritance symmetry in general relativity

In an earlier paper published by Bokhari et al., Nuovo Cimento B, 118 (2003) 803, a complete classification of spherically symmetric static space-times according to their Ricci inheritance symmetries was given. It was shown that such space-times admit non-trivial Ricci inheritance symmetries if their metrics satisfy some non-linear differential constraints. However because of the non-linearity of differential constraints no example of a space-time was provided where it could have been tested if such symmetry would exist realistically. Thus whereas the classification of Ricci inheritance was provided, one most important aspect was left unresolved by not giving examples to support the claim if there would be any spherically symmetric static geometries that will host such a symmetry? In this paper we have tried to provide an answer to this question by considering some well-known specific spherically symmetric static metrics. It is shown that none of these chosen metrics possess any non-trivial Ricci inheritance symmetry of finite-dimensional Lie algebras. We summarize these results in the form of a conjecture.