Kerr-Schild-Kundt Metrics in Generic Gravity Theories with Modified Horndeski Couplings

TL;DR

This paper investigates the universality of Kerr-Schild-Kundt metrics within Modified Horndeski gravity theories coupled with electromagnetic fields, providing exact solutions for specific wave configurations in arbitrary dimensions.

Contribution

It extends the universality theorem of KSK metrics to Modified Horndeski theories with Maxwell fields, deriving exact wave solutions in arbitrary dimensions.

Findings

Derived exact $pp$-wave solutions in Modified Horndeski theories.

Obtained AdS-plane wave solutions in arbitrary dimensions.

Extended the universality of KSK metrics to theories with matter fields.

Abstract

The Kerr-Schild-Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order covariant derivatives. There is yet no complete proof that these metrics are universal in the presence of matter fields such as electromagnetic and/or scalar fields. In order to get some insight into what happens when we extend the "universality theorem" to the case in which the electromagnetic field is present, as a first step, we study the KSK class of metrics in the context of Modified Horndeski theories with Maxwell's field. We obtain exact solutions of these theories representing the $pp$-waves and AdS-plane waves in arbitrary $D$ dimensions.