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.
Highlights
The exact symmetries in a general relativity framework are usually known as isometries that are given by Killing vectors
We find the principal tensor of these near-horizon extremal/extremal vanishing horizon (EVH) geometries
We studied the principal and Killing tensors of near-horizon extremal and EVH geometries of a Kerr-AdS-NUT black hole in odd dimensions
Summary
The exact symmetries in a general relativity framework are usually known as isometries that are given by Killing vectors. There are special extremal black holes for which the symmetry enhances more in their nearhorizon geometries They are called extremal vanishing horizon (EVH) black holes [16] and have been studied in Refs. We start by studying the near-horizon geometry of odd-dimensional Kerr-AdS-NUT black holes in both extremal and EVH limits.. The Killing tensors and their reduction to Killing vectors of near-horizon geometries has been studied in Refs. S. SADEGHIAN study the separability of timelike geodesic equations on near-horizon extremal/EVH geometries of Kerr-AdS-NUT black holes, explicitly. Finding the constants of motion, we infer that timelike geodesics on the corresponding background metrics are integrable
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