SUSY in the Spacetime of Higher-Dimensional Rotating Black Holes

TL;DR

This paper explores the hidden symmetries of higher-dimensional rotating black holes using supersymmetric mechanics, revealing new supercharges and their algebraic structures that lead to conserved quantities.

Contribution

It introduces two nontrivial supercharges related to Killing-Yano tensors in higher-dimensional black holes, expanding understanding of their symmetry structures.

Findings

Identification of supercharges from Killing-Yano tensors

Extended Poisson-Dirac algebra of supercharges

Explicit examples for D=6 Myers-Perry black holes

Abstract

General higher-dimensional rotating black hole spacetimes of any dimensions admit the Killing and Killing-Yano tensors, which generate the hidden symmetries just as in four-dimensional Kerr spacetime. We study these properties of the black holes using the formalism of supersymmetric mechanics of pseudo-classical spinning point particles. We present two nontrivial supercharges, corresponding to the Killing-Yano and conformal Killing-Yano tensors of the second rank. We demonstrate that an unusual extended Poisson-Dirac algebra of these supercharges results in two independent Killing tensors in spacetime dimensions $ D\geq 6 $, giving explicit examples for the Myers-Perry black holes in $ D = 6 $ dimensions.