Higher-dimensional black holes: hidden symmetries and separation of variables

By Valeri P. Frolov, D. Kubizňák. 2008

143 citations recorded by the source corpus.

In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing–Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing–Yano 2-form) in 4D flat spacetime one can ‘generate’ the 4D Kerr–NUT–(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr–NUT–(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing–Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton–Jacobi, Klein–Gordon and Dirac equations in the general Kerr–NUT–(A)dS metrics.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/215d14b1f0fa2e2f56c3b6cab1351a54488990fc

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Citations in the corpus

Black hole chemistry: thermodynamics with Lambda (2016, background): “In any dimension, the general rotating KerrAdS geometry admits a hidden symmetry of the Killing–Yano tensor [293] that is responsible for integrability of geodesic motion and various test field equations in these spacetimes [294].”