Einstein-Yang-Mills-Lorentz black holes

TL;DR

This paper explores black hole solutions in Einstein-Yang-Mills-Lorentz theory, revealing their equivalence to certain extended gravitational models by identifying gauge and spin connections, and providing exact solutions.

Contribution

It introduces a novel approach linking gauge Lorentz group solutions to extended gravitational theories through an ansatz that equates gauge and spin connections.

Findings

Exact solutions to Einstein-Yang-Mills-Lorentz equations are found.

The gauge Lorentz group solutions are shown to be equivalent to extended gravitational theories.

The approach simplifies the analysis of black holes in gauge theories of gravity.

Abstract

Different black hole solutions of the coupled Einstein-Yang-Mills equations have been well known for a long time. They have attracted much attention from mathematicians and physicists since their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows one to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories.