Birkhoff Theorem and Matter

TL;DR

This paper demonstrates that Birkhoff's theorem approximately holds in spherically symmetric spacetimes that are nearly vacuum, extending its applicability to more realistic, imperfect conditions in general relativity.

Contribution

It proves the converse of previous work, showing the theorem's robustness in nearly vacuum, spherically symmetric spacetimes, broadening its practical relevance.

Findings

Birkhoff's theorem remains approximately valid in nearly vacuum conditions.

The theorem's applicability extends to realistic, imperfect spherical symmetry.

Supports the use of Birkhoff's theorem in more practical astrophysical scenarios.

Abstract

Birkhoff's theorem for spherically symmetric vacuum spacetimes is a key theorem in studying local systems in general relativity theory. However realistic local systems are only approximately spherically symmetric and only approximately vacuum. In a previous paper, we showed the theorem remains approximately true in an approximately spherically symmetric vacuum space time. In this paper we prove the converse case: the theorem remains approximately true in a spherically symmetric, approximately vacuum space time.