Scalar-tensor representation of $f(R)$ gravity and Birkhoff's theorem

Understand

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.