Symmetry Inheritance and Jebsen-Birkhoff Theorem

TL;DR

This paper investigates the conditions under which the Jebsen-Birkhoff theorem applies to non-vacuum solutions in various gravitational theories by analyzing symmetry inheritance properties.

Contribution

It provides a detailed analysis of the additional constraints fields must satisfy for the theorem to hold beyond vacuum cases.

Findings

Identifies specific symmetry inheritance conditions for non-vacuum solutions.

Extends understanding of the Jebsen-Birkhoff theorem to broader gravitational theories.

Abstract

It is known that the Jebsen-Birkhoff theorem is valid for vacuum solutions to Einstein's equation, as well as some of its generalizations. Using symmetry inheritance properties we investigate in detail the additional constraints that fields have to satisfy in order to allow the Jebsen-Birkhoff theorem in the non-vacuum cases of a wide class of gravitational field equations.