Vacuum Kerr-Schild metrics generated by nontwisting congruences

Abstract

The Kerr-Schild pencil of metrics ${\tilde{g}}_{ab}=g_{ab}+V{l}_a{l}_b$, 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 Kóta-Perjés metrics. The base space-time is a pp-wave.

12 pages

References in corpus (3)

• Kerr-Schild metrics revisited I. The ground state
• Kerr-Schild metrics revisited II. The complete vacuum solution
• Solution of the vacuum Kerr-Schild problem

Cited by in corpus (6)

• Linear Einstein equations and Kerr-Schild maps
• New framework for classical double copies
• Avenues for Analytic exploration in Axisymmetric Spacetimes. Foundations and the Triad Formalism
• K-essence sources of Kerr-Schild spacetimes
• Exact Kerr--Schild spacetimes from linearized kinetic gravity braiding
• Quasilocal energy exchange and the null cone