Conformal frames and the validity of Birkhoff's theorem

TL;DR

This paper investigates the validity of Birkhoff's theorem within scalar-tensor theories of gravity, comparing Einstein and Jordan frames, and questions their physical equivalence in perturbative regimes.

Contribution

It provides a perturbative analysis of Birkhoff's theorem in scalar-tensor theories and examines the differences between Einstein and Jordan frames.

Findings

Birkhoff's theorem does not generally hold in scalar-tensor theories.

The Einstein and Jordan frames show differences in perturbative validity.

Results challenge the physical equivalence of the two frames in perturbations.

Abstract

Birkhoff's theorem is one of the most important statements of Einstein's general relativity, which generally can not be extended to modified theories of gravity. Here we study the validity of the theorem in scalar-tensor theories using a perturbative approach, and compare the results in the so-called Einstein and Jordan frames. The implications of the results question the physical equivalence between both frames, at least in perturbations.