Twisted Gravitational Waves of Petrov Type D

TL;DR

This paper explicitly studies a special class of twisted gravitational waves of Petrov type D, deriving their properties, symmetries, and limits to plane waves, expanding understanding of nonplanar Ricci-flat solutions in general relativity.

Contribution

It introduces and analyzes a new explicit class of Petrov type D twisted gravitational wave solutions depending on an arbitrary function, including their symmetries and plane-wave limits.

Findings

Derived Killing vectors for the Petrov type D solutions.

Analyzed the Harrison and w-metric solutions.

Determined their Penrose plane-wave limits.

Abstract

Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat solutions of general relativity. Thus far only TGWs of Petrov type \emph{II} are implicitly known that depend on a solution of a partial differential equation and have wave fronts with negative Gaussian curvature. A special Petrov type \emph{D} class of such solutions that depends on an arbitrary function is explicitly studied in this paper and its Killing vectors are worked out. Moreover, we concentrate on two solutions of this class, namely, the Harrison solution and a simpler solution we call the $w$-metric and determine their Penrose plane-wave limits. The corresponding transition from a nonplanar TGW to a plane gravitational wave is elucidated.