New Almost Universal Metrics

TL;DR

This paper introduces a new class of almost universal metrics, specifically nonzero constant curvature pp-waves, which simplify complex gravitational equations to more manageable forms, expanding the known universality classes.

Contribution

The authors identify and demonstrate that nonzero constant curvature pp-waves are almost universal metrics, extending the Kerr-Schild-Kundt class and linking to important cosmological solutions.

Findings

Nonzero constant curvature pp-waves reduce gravity equations to Einstein-Maxwell with null dust.

These metrics connect to Nariai and Bertotti-Robinson solutions with specific topologies.

The results are exemplified in quadratic and cubic gravity theories.

Abstract

Plane waves and pp-waves are well-known universal metrics that solve all metric-based gravitational field equations. Similarly, the Kerr-Schild-Kundt class of metrics is almost universal: all metric-based gravitational field equations reduce to a linear scalar partial differential equation that always admits a solution. Here, we add a new member to this class of metrics and show that nonzero constant curvature pp-wave metrics are also almost universal. They reduce the generic gravity field equations to those of cosmological Einstein-Maxwell theory with null dust. The background of the pp-waves has the topology $\mathbb{R}^{1,1}\times S^{2}$ and provides the missing partner to the Nariai metric with ${\rm dS}^{2}\times S^{2}$ and the Bertotti-Robinson metric with ${\rm AdS}^{2}\times S^{2}$ topologies. These quantum-protected metrics are of clear interest. We exemplify our results by using the quadratic and cubic gravity theories.