Symmetries of supergravity black holes

TL;DR

This paper explores the symmetries of supergravity black holes by analyzing Killing tensors, revealing conditions under which separability and explicit tensor expressions occur in various supergravity solutions.

Contribution

It provides new explicit forms of conformal Killing-Stackel tensors for supergravity black holes and demonstrates their relation to separability of key equations.

Findings

Explicit conformal Killing-Stackel tensors derived for specific black hole solutions.

Separation of Hamilton-Jacobi and Klein-Gordon equations verified on related metrics.

Simplified solutions when charges are equal, facilitating analysis.

Abstract

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.