New Exact Solutions of Quadratic Curvature Gravity

TL;DR

This paper extends known properties of Kerr-Schild solutions to quadratic curvature gravity in arbitrary dimensions, presenting a new exact spherical wave solution in an AdS background within this class.

Contribution

It demonstrates that Kerr-Schild solutions satisfy both exact and linearized field equations in quadratic gravity and introduces a novel spherical wave solution in this context.

Findings

Kerr-Schild solutions satisfy both exact and linearized equations in quadratic gravity.

A new exact spherical wave solution in AdS background is constructed.

The solution belongs to Kundt spacetimes with constant curvature invariants.

Abstract

It is a known fact that the Kerr-Schild type solutions in general relativity satisfy both exact and linearized Einstein field equations. We show that this property remains valid also for a special class of the Kerr-Schild metrics in arbitrary dimensions in generic quadratic curvature theory. In addition to the AdS-wave (or Siklos) metric which represents plane waves in an AdS background, we present here a new exact solution, in this class, to the quadratic gravity in D-dimensions which represents a spherical wave in an AdS background. The solution is a special case of the Kundt metrics belonging to spacetimes with constant curvature invariants.