Spherically symmetric solutions of modified field equations in f(R) theories of gravity

Abstract

Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In particular, we show that for a large class models, including e.g. the f(R)=R-\mu^4/R model, the Schwarzschild-de Sitter metric is an exact solution of the field equations. The significance of these solutions is discussed in light of solar system constraints on $f(R)$ theories of gravity.