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.
Highlights
The Kerr–Schild–Kundt (KSK) metrics belong to a very special type-N metrics in general relativity
In the case of the KSK metrics, the field equations of the generic theory defined by the action (1) reduce to a system of coupled linear partial differential equations
N is related to the number of covariant derivatives of the Riemann tensor that may appear in the f function of a generic gravity theory
Summary
The Kerr–Schild–Kundt (KSK) metrics belong to a very special type-N metrics in general relativity. Our main goal in the present work is to extend these works to the KSK metrics In this direction, as a first step, we shall consider a generic theory of gravity coupled with Horndeski-type [13] interaction and a modification of it. In the case of the KSK metrics, the field equations of the generic theory defined by the action (1) reduce to a system of coupled linear partial differential equations. N is related to the number of covariant derivatives of the Riemann tensor that may appear in the f function of a generic gravity theory. The constants an’s in (5) are functions of the parameters of the explicit gravity theory at hand, and the linear operator O appearing in (5) is defined in (42) in Sect. To see the simplification introduced by the KSK metrics, let us give the following two specific examples
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