The Kerr-Schild ansatz for the Nariai spacetime and the generating conjecture

TL;DR

This paper demonstrates that the Nariai spacetime can be expressed as a conformally Kerr-Schild metric and finds new Einstein-Maxwell solutions using the Horsky-Mitskievich generating conjecture.

Contribution

It introduces a conformally Kerr-Schild representation for the Nariai spacetime and applies the generating conjecture to derive new Einstein-Maxwell solutions.

Findings

Nariai metric admits a conformally Kerr-Schild form

New Einstein-Maxwell solutions for Nariai spacetime are obtained

The generating conjecture is effectively applied to this spacetime

Abstract

We will show that the Nariai metric, i.e. the static spherically symmetric vacuum spacetime with a cosmological constant, admits a conformally Kerr-Schild spacetime representation. We find the vacuum solutions of the Einstein-Maxwell equations for the Nariai metric using the Horsky-Mitskievich generating conjecture.