Locally Rotationally Symmetric Vacuum Solutions in f(R) Gravity

Abstract

This paper is devoted to find the Locally Rotationally Symmetric (LRS) vacuum solutions in the context of f(R) theory of gravity. Actually, we have considered the three metrics representing the whole family of LRS spacetimes and solved the field equations by using metric approach as well as the assumption of constant scalar curvature. It is mention here that R may be zero or non-zero. In all we found 10 different solutions.