Separability, plane wave limits and black holes

TL;DR

This paper develops a systematic method to construct Penrose coordinates and plane wave limits for spacetimes with separable null Hamilton-Jacobi and geodesic equations, applied to Kerr-NUT-(A)dS black holes and near horizon geometries.

Contribution

It introduces a general approach for deriving plane wave limits in complex black hole spacetimes with separable equations, expanding understanding of near horizon geometries.

Findings

Plane wave limits of Kerr-NUT-(A)dS black holes are constructed.

Near horizon geometries of extreme black holes admit Minkowski spacetime as a plane wave limit.

Method is demonstrated explicitly for four-dimensional black holes.

Abstract

We present a systematic construction of the Penrose coordinates and plane wave limits of spacetimes for which both the null Hamilton-Jacobi and geodesic equations separate. The method is illustrated for the Kerr-NUT-(A)dS four-dimensional black holes. The plane wave limits of the near horizon geometry of the extreme Kerr black hole are also explored. All near horizon geometries of extreme black holes with a Killing horizon admit Minkowski spacetime as a plane wave limit.