# Birkhoff's Theorem for Quasi-Metric Gravity

## TL;DR

This paper investigates whether Birkhoff's theorem holds in quasi-metric gravity and finds that it does, although the proof differs from the general relativistic case, confirming the static nature of the exterior gravitational field.

## Contribution

It demonstrates that Birkhoff's theorem applies within the quasi-metric framework, providing a novel proof distinct from the general relativity approach.

## Key findings

- Birkhoff's theorem holds in quasi-metric gravity.
- The exterior gravitational field of a spherically symmetric body is necessarily static.
- The proof differs from the general relativistic case.

## Abstract

Working within the quasi-metric framework (QMF), it is examined if the gravitational field exterior to an isolated, spherically symmetric body is necessarily metrically static, or equivalently, whether or not Birkhoff's theorem holds for quasi-metric gravity. It is found that it does; however the proof is somewhat different from the general-relativistic case.