Separability of Black Holes in String Theory

TL;DR

This paper investigates the mathematical structures underlying the separability of equations in rotating black holes within string theory, identifying conditions for enhanced symmetries and their relation to black hole types.

Contribution

It constructs and analyzes conformal Killing-Stackel tensors for various black holes, revealing when exact or enhanced symmetries occur, especially highlighting the uniqueness of Kerr-Newman black holes.

Findings

Kerr-Newman black holes admit an exact Killing-Stackel tensor.

Two-charge black holes can have an enhanced conformal Killing-Stackel tensor.

Rotating Kaluza-Klein black holes have a conformal Killing-Stackel tensor but no further symmetry enhancements.

Abstract

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)^2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.