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

Abstract

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

Notes on emergent conformal symmetry for black holes

“…near-ring region when acting on the eikonal massless scalar field. It would be interesting to explore whether a similar correspondence exists for the extremal near-horizon geometry of the accelerating black hole [72] and the Taub-NUT black hole [73]. Furthermore, based on our investigations in this paper, we propose that the Love symmetry [74][75][76][77][78][79], Ladder symmetry [80,81], and near-zone symmetry [82] may be preserved by spacetimes without Z 2 symmetry.…”

Rotating and charged Taub-NUT-(A)dS spacetimes on a 3-brane

“…This solution is a special case of Plebanski-Demianski solution [36,37] that has parameters of mass, electric charge, rotation, NUT, and cosmological constant. With or without the electric charge and cosmological constant in the discussions, this solution has been studied rigorously in literature [38,39,40,41,42,43,44,45,46,47]. Despite the irregularity of spacetime with NUT parameter on its rotational axis [48,49,50], most aspects of this type of spacetime resemble those of black holes [54,53,52,51,55].…”