Generalized Birkhoff theorem in the Poincar\'e gauge gravity theory

TL;DR

This paper extends Birkhoff's theorem to Poincaré gauge gravity, analyzing spherically symmetric solutions within models that include quadratic curvature and torsion invariants, identifying conditions for the theorem's validity.

Contribution

It introduces a generalized Birkhoff theorem in Poincaré gauge gravity, considering the most general quadratic Lagrangians with parity-even and odd sectors.

Findings

Identifies models where the weak Birkhoff theorem holds.

Identifies models where the strong Birkhoff theorem holds.

Uses double duality technique to analyze solutions.

Abstract

The analysis of the validity of Birkhoff's theorem about the uniqueness of the spherically symmetric solution of the gravitational field equations is extended to the framework of the Poincar\'e gauge gravity theory. The class of models with the most general Lagrangians of the Yang-Mills type constructed from all possible quadratic invariants of the curvature and the torsion is considered, including both parity-even and parity-odd sectors. We find the models in which the weak and strong versions of the generalized Birkhoff theorem are valid, by making use of the double duality technique.