Static spherically symmetric perfect fluid solutions in f(R) theories of gravity

Static spherically symmetric perfect fluid solutions are studied in metric f(R) theories of gravity. We show that pressure and density do not uniquely determine f(R) i.e. given a matter distribution and an equation state, one cannot determine the functional form of f(R). However, we also show that matching the outside Schwarzschild-de Sitter metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.