Extremal Kerr-Schild Form

TL;DR

This paper introduces a new extremal Kerr-Schild ansatz that generalizes the form to include various black hole solutions with matter, potentially advancing perturbation theory, solution construction, and holographic studies.

Contribution

It presents a generalized extremal Kerr-Schild form applicable to diverse black holes with matter, beyond algebraic type restrictions, enabling broader analytical and solution-generating techniques.

Findings

Applicable to charged Kerr-NUT-(A)dS spacetimes

Extends to black holes in minimal gauged supergravity

Useful for black hole perturbation and solution construction

Abstract

We propose a novel ansatz, where the full black hole geometry is written as a linear in mass perturbation of the associated extremal black hole base. Contrary to its "standard" version, the corresponding "extremal Kerr-Schild form" is no longer restricted to special algebraic type spacetimes, and is applicable to numerous black hole solutions with matter, such as the charged Kerr-NUT-(A)dS spacetimes, black holes of $D=5$ minimal gauged supergravity, or the charged dilaton-axion rotating solutions. This ansatz is likely to find its applications in black hole perturbation theory, shed new light on the CFT description of non-extremal black holes, as well as be useful for constructing new exact solutions.