Anti-de Sitter gauge theory for gravity

TL;DR

This paper explores a gauge theory of gravity based on the anti-de Sitter group, deriving field equations, conservation laws, and discussing solutions, including implications for cosmology and black hole solutions.

Contribution

It introduces a Yang-Mills gauge theory framework for gravity using the SO(2,3) group, extending Einstein-Cartan theory with new field equations and solutions.

Findings

Early universe as the only RW-geometry solution with perfect fluid

No Schwarzschild solutions in torsion-free vacuum when curvature squared terms are neglected

Conservation laws derived from Bianchi identities for anti-de Sitter gravity

Abstract

First a review is given of Riemann-Cartan space-time and Einstein-Cartan gravity. This gives us the necessary tools to handle the SO(2,3) Yang-Mills gauge theory for gravity. Field equations are obtained from a Yang-Mills gauge field Lagrangian. From these field equations and the Bianchi identities the conservation laws for anti-de Sitter theory are derived. Possible solutions of the field equations are discussed. The only solution found for a RW-geometry with a perfect fluid matter content is the early universe. There are no Schwarzschild solutions of the torsion free vacuum field equations if curvature squared terms cannot be neglected.