Vacuum Kerr-Schild metrics generated by nontwisting congruences

TL;DR

This paper investigates vacuum Kerr-Schild metrics generated by nontwisting null congruences, revealing solutions including Kasner and Kóta-Perjés metrics derived from pp-wave spacetimes.

Contribution

It characterizes vacuum Kerr-Schild metrics with nontwisting null vectors, identifying specific solutions and their relation to known cosmological and wave spacetimes.

Findings

Identified Kasner and Kóta-Perjés metrics within this class.

Connected solutions to pp-wave spacetimes.

Demonstrated the role of nontwisting null congruences in vacuum solutions.

Abstract

The Kerr-Schild pencil of metrics $\tilde g_{ab}=g_{ab}+V l_al_b$, with $g_{ab}$ and $\tilde g_{ab}$ satisfying the vacuum Einstein equations, is investigated in the case when the null vector $l$ has vanishing twist. This class of Kerr-Schild metrics contains two solutions: the Kasner metric and a metric wich can be obtained from the Kasner metric by a complex coordinate transformation. Both are limiting cases of the K\'ota-Perj\'es metrics. The base space-time is a pp-wave.