Stationary generalized Kerr-Schild spacetimes

TL;DR

This paper introduces a new family of stationary perfect-fluid solutions to Einstein's equations using generalized Kerr-Schild transformations, expanding the known solutions in algebraically special spacetimes.

Contribution

It develops a novel method combining null and timelike vector techniques to find broader stationary solutions, including the Kerr metric in Einstein Universe background.

Findings

Includes all classical vacuum Kerr-Schild spacetimes except plane-fronted waves

Family depends on an arbitrary function of one variable

Analyzes properties in a coordinate-free manner

Abstract

In this paper we have applied the generalized Kerr-Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike vector fields, from which some properties of the solutions are studied in a coordinate-free way. These spacetimes are algebraically special being their Petrov types II and D. This family includes all the classical vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves, and some other interesting solutions as, for instance, the Kerr metric in the background of the Einstein Universe. However, the family is much more general and depends on an arbitrary function of one variable.