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New Almost Universal Metrics

Metin Gurses, Tahsin Cagri Sisman, Bayram Tekin

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.

New Almost Universal Metrics

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 and provides the missing partner to the Nariai metric with and the Bertotti-Robinson metric with topologies. These quantum-protected metrics are of clear interest. We exemplify our results by using the quadratic and cubic gravity theories.

Paper Structure

This paper contains 3 sections, 10 theorems, 76 equations.

Table of Contents

  1. Example 1--Quadratic gravity
  2. Example 2--Cubic gravity generated by string theory
  3. Conclusions

Key Result

Theorem 1

The metric satisfies the cosmological Einstein-Maxwell field equations for the electromagnetic four-potential where $\lambda_{\mu}=\partial_{\mu}u$, and $\Lambda$ is a positive cosmological constant. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Corollary 1
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Corollary 2
  • Theorem 8