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.
Classical and Quantum Gravity
- Pub Date:
- August 2008
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- 33 pages, no figures, updated references and corrected typos