Correspondence between Einstein-Yang-Mills-Lorentz systems and dynamical torsion models

TL;DR

This paper establishes a correspondence between Einstein-Yang-Mills theories with gauge Lorentz groups and torsion theories in Riemann-Cartan space-times, simplifying the search for exact solutions.

Contribution

It introduces a novel method linking Einstein-Yang-Mills systems to torsion models, enabling easier derivation of exact solutions.

Findings

Derived explicit solutions using the correspondence

Applied the method to SO(1,n-1) and SO(n-2) groups

Provided an alternative approach to known solutions

Abstract

In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular correspondence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is specially useful in order to simplify the problem of finding exact solutions to the Einstein-Yang-Mills equations. The applicability of the method is divided into two approaches: one associated with the Lorentz group SO(1,n-1) of the space-time rotations and another one with its subgroup SO(n-2). Solutions for both cases are presented by the explicit use of this correspondence and, interestingly, for the last one by imposing on our ansatz the same kind of rotation and reflection symmetry properties as for a nonvanishing space-time torsion. Although these solutions were found in previous literature by a different approach, our method provides an alternative way to obtain them and it may be used in future research to find other exact solutions within this theory.