New class of non-Einstein pp-wave solutions to quadratic gravity

TL;DR

This paper introduces a new family of exact vacuum solutions in quadratic gravity describing pp-waves with wave surfaces of any constant curvature, extending known solutions and revealing non-Einstein geometries.

Contribution

The authors derive a new class of exact solutions to quadratic gravity with curved wave surfaces, generalizing previous flat wave solutions and explicitly solving the linear biharmonic equation involved.

Findings

Solutions include flat and curved wave surfaces with constant curvature.

Curvature is linearly related to the cosmological constant.

Explicit examples of solutions are provided.

Abstract

We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves obtained by Madsen, a subset of which forms precisely the vacuum pp-waves of general relativity. If, on the other hand, the wave surfaces have non-vanishing constant curvature then all our solutions are non-Einstein (i.e. they do not solve Einstein's equations in vacuum, with or without cosmological constant) and we find that the curvature is linearly related to the value of the cosmological constant. We show that the vacuum field equations reduce to a simple linear biharmonic equation on the curved wave surfaces, and as consequence, the general solution can be written down. We also provide some simple explicit examples.