Torsion Wave Solutions in Yang-Mielke Theory of Gravity

TL;DR

This paper develops explicit torsion wave solutions within the Yang-Mielke theory of gravity, a metric-affine gravity framework based on a Yang-Mills action for the affine connection, and compares them to existing solutions.

Contribution

It introduces explicit torsion wave solutions in Yang-Mielke gravity, expanding the set of known solutions in metric-affine theories with a Yang-Mills structure.

Findings

Constructed explicit pp-metric spacetimes with axial torsion

Demonstrated these spacetimes solve the Yang-Mills equations in this theory

Compared new solutions with existing metric-affine gravity solutions

Abstract

The approach of metric-affine gravity initially distinguishes it from Einstein's general relativity. Using an independent affine connection produces a theory with 10+64 unknowns. We write down the Yang-Mills action for the affine connection and produce the Yang-Mills equation and the so called complementary Yang-Mills equation by independently varying with respect to the connection and the metric respectively. We call this theory the Yang-Mielke theory of gravity. We construct explicit spacetimes with pp-metric and purely axial torsion and show that they represent a solution of Yang-Mills theory. Finally we compare these spacetimes to existing solutions of metric-affine gravity and present future research possibilities.