Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables

Feb, 2008
33 pages
Published in:
  • Class.Quant.Grav. 25 (2008) 154005
e-Print:
Report number:
  • ALBERTA-THY-02-08

Citations per year

20082012201620202024051015
Abstract: (arXiv)
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' 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.
Note:
  • 33 pages, no figures
  • 04.70.Bw
  • 04.50.+h
  • 04.20.Jb
  • tensor: Killing
  • black hole: rotation
  • black hole: higher-dimensional
  • Dirac equation
  • space-time: de Sitter
  • geodesic
  • integrability