AdS-plane wave and pp-wave solutions of generic gravity theories

TL;DR

This paper constructs AdS-plane wave and pp-wave solutions for a broad class of gravity theories involving arbitrary powers of the Riemann tensor and derivatives, extending known solutions and analyzing their properties.

Contribution

It provides a general formalism for wave solutions in generic gravity theories, including explicit solutions in quadratic, conformal, tricritical, Lanczos-Lovelock, and string-inspired cubic curvature gravities.

Findings

Wave solutions can be expressed using the traceless-Ricci tensor.

Explicit solutions are derived for multiple gravity theories.

The formalism unifies wave solutions across various higher-curvature theories.

Abstract

We construct the AdS-plane wave solutions of generic gravity theory built on the arbitrary powers of the Riemann tensor and its derivatives in analogy with the pp-wave solutions. In constructing the wave solutions of the generic theory, we show that the most general two tensor built from the Riemann tensor and its derivatives can be written in terms of the traceless-Ricci tensor. Quadratic gravity theory plays a major role; therefore, we revisit the wave solutions in this theory. As examples to our general formalism, we work out the six-dimensional conformal gravity and its nonconformal deformation as well as the tricritical gravity, the Lanczos-Lovelock theory, and string-generated cubic curvature theory.