Love symmetry in higher-dimensional rotating black hole spacetimes

TL;DR

This paper introduces a method to construct Love symmetry generators in higher-dimensional rotating black hole spacetimes, focusing on the horizon vicinity to reveal hidden symmetries and separability of scalar wave equations.

Contribution

The paper develops a novel approach to identify Love symmetries in higher-dimensional rotating black holes, extending previous 4D and 5D results to a broad class of spacetimes.

Findings

Constructed a 1-parameter family of Love symmetry generators near the horizon.

Demonstrated separability of the scalar wave equation in Myers--Perry-like coordinates.

Showed separability also occurs in horizon-penetrating Painlevé--Gullstrand coordinates.

Abstract

We develop a method for constructing a 1-parameter family of globally-defined Love symmetry generators in rotating black hole spacetimes of general dimension. The key ingredient is to focus on the vicinity of the (physical) outer horizon, matching only the radial derivative and the outer horizon pole pieces of the Klein--Gordon operator in the black hole spacetime to the $SL(2,\mathbb{R})$ Casimir operator. After revisiting the 4D Kerr and 5D Myers--Perry cases, the procedure is illustrated on generalized Lense--Thirring spacetimes which describe a wide variety of slowly rotating black hole metrics in any number of dimensions. Such spacetimes are known to admit an extended tower of Killing tensor and Killing vector symmetries and, as demonstrated in this paper, allow for separability of the massive scalar wave equation in Myers--Perry-like coordinates. Interestingly, separability also occurs in the horizon-penetrating Painlev{\'e}--Gullstrand coordinates associated with the freely infalling observer who registers flat space around her all the way to singularity.