The Jebsen-Birkhoff theorem in alternative gravity

TL;DR

This paper examines the applicability of the Jebsen-Birkhoff theorem in scalar-tensor theories of gravity, clarifying apparent contradictions and extending its validity to various modified gravity models.

Contribution

It generalizes the Jebsen-Birkhoff theorem for scalar-tensor theories and clarifies contradictions with Hawking's theorem in different frames and gravity models.

Findings

The theorem's validity varies across different scalar-tensor theories.

Contradictions with Hawking's theorem are resolved in the context of these theories.

Applications to f(R) gravity demonstrate the theorem's broader relevance.

Abstract

We discuss the validity, or lack thereof, of the Jebsen-Birkhoff theorem in scalar-tensor theories by generalizing it and regarding the Brans-Dicke-like scalar as effective matter. Both the Jordan and Einstein frames are discussed and an apparent contradiction between static spherical solutions of scalar-tensor gravity and Hawking's theorem on Brans-Dicke black holes is clarified. The results are applied to metric and Palatini f(R) gravity.