  Birkhoff's theorem is discussed in the frame of f(R) gravity by using its
scalar-tensor representation. Modified gravity has become very popular at
recent times as it is able to reproduce the unification of inflation and
late-time acceleration with no need of a dark energy component or an inflaton
field. Here, another aspect of modified f(R) gravity is studied, specifically
the range of validity of Birkhoff's theorem, compared with another alternative
to General Relativity, the well known Brans-Dicke theory. As a novelty, here
both theories are studied by using a conformal transformation and writing the
actions in the Einstein frame, where spherically symmetric solutions are
studied by using perturbation techniques. The differences between both theories
are analyzed as well as the validity of the theorem within the Jordan and
Einstein frames, where interesting results are obtained.

General Relativity and Quantum Cosmology;High Energy Physics - Theory