Hidden symmetries of near-horizon extremal Kerr-AdS-NUT geometries

TL;DR

This paper investigates the hidden symmetries of near-horizon geometries of extremal Kerr-AdS-NUT black holes, demonstrating integrability and separability of geodesic equations through explicit Killing tensor analysis.

Contribution

It explicitly derives and verifies the Killing tensors and constants of motion for near-horizon extremal Kerr-AdS-NUT geometries, revealing their hidden symmetries.

Findings

Geodesic equations are separable and integrable in these geometries.

Killing tensors are explicitly constructed from constants of motion.

Near horizon Killing tensors match those obtained from the limit.

Abstract

We study hidden symmetries, the symmetries associated with the Killing tensors, of the near horizon geometry of odd-dimensional Kerr-AdS-NUT black hole in two limits: generic extremal and extremal vanishing horizon (EVH) limits. Starting from Kerr-AdS-NUT black hole in ellipsoidal coordinates which admits integrable geodesic equations, we obtain the near horizon extremal/EVH geometries and their principal and Killing tensors by taking the near horizon limit. We explicitly demonstrate that geodesic equations are separable and integrable on theses near horizon geometries. We also compute the constants of motion and read the Killing tensors of these near horizon geometries from the constants of motion. As we expected, they are the same as the Killing tensors given by taking the near horizon limit.