Birkhoff for Lovelock Redux

TL;DR

This paper proves that all metric theories with second order field equations, including Lovelock theories, satisfy Birkhoff's theorem, ensuring their spherically symmetric solutions are static, which has implications for gravitational theory consistency.

Contribution

It establishes Birkhoff's theorem for Lovelock and similar metric theories with second order field equations, extending previous results.

Findings

All such theories have static spherically symmetric solutions.

The proof simplifies understanding of gravitational solutions in these theories.

Supports the universality of Birkhoff's theorem across a broad class of metric theories.

Abstract

We show succinctly that all metric theories with second order field equations obey Birkhoff's theorem: their spherically symmetric solutions are static.