Torsion Wave Solutions in Yang-Mielke Theory of Gravity

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.

Axial torsion waves in metric-affine gravity

“…Torsion (10), (11) corresponds to the axial torsion first obtained by Singh. Note that the connection of a generalised pp-wave with purely axial torsion is metric compatible, i.e.…”

Physical interpretation of pp-waves with axial torsion

“…1, 2 In our previous paper Ref. 4, we introduced generalised pp-waves with purely axial torsion as metric compatible spacetimes with pp-metric and torsion T := * A, where A is a real vector field defined by A = k(ϕ)l, where l is a real parallel null lightlike vector and k : R → R is an arbitrary real function of the phase ϕ : M → R, ϕ(x) := l · dx. If we were to write down the pp-metric locally as…”

pp-waves in modified gravity

“…The general quadratic curvature gravity leads to a set of fourth order field equations and naturally, there are not as many exact solutions as in the general theory of relativity. The gravitational wave solutions to the quadratic curvature (QC) gravity has been studied in [156,157,162,163] and recently in [164][165][166] in the more general setting of metric-affine gravity. The QC gravity has a long history [167] initiated shortly after the introduction of GR.…”