A new framework for studying spherically symmetric static solutions in
  f(R) gravity
  We develop a new covariant formalism to treat spherically symmetric
spacetimes in metric} f(R) theories of gravity. Using this formalism we derive
the general equations for a static and spherically symmetric metric in a
general f(R)-gravity. These equations are used to determine the conditions for
which the Schwarzschild metric is the only vacuum solution with vanishing Ricci
scalar. We also show that our general framework provides a clear way of showing
that the Schwarzschild solution is not a unique static spherically symmetric
solution, providing some incite on how the current form of Birkhoff's theorem
breaks down for these theories.
