Kerr-Schild spacetimes with (A)dS background

TL;DR

This paper investigates the properties of Kerr-Schild spacetimes with (A)dS backgrounds across various dimensions, classifying their algebraic types and analyzing their optical and curvature characteristics.

Contribution

It provides a comprehensive analysis of Kerr-Schild spacetimes with (A)dS backgrounds, including classification by Weyl type and solutions to the Sachs equation.

Findings

Non-expanding Kerr-Schild spacetimes are of Weyl type N.

Expanding Kerr-Schild spacetimes are of type II or D.

The optical constraint is satisfied, enabling explicit solutions.

Abstract

General properties of Kerr-Schild spacetimes with (A)dS background in arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes with non-expanding k are shown to be of Weyl type N, while the expanding spacetimes are of type II or D. It is shown that this class of spacetimes obeys the optical constraint. This allows us to solve Sachs equation, determine r-dependence of boost weight zero components of the Weyl tensor and discuss curvature singularities.