Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background

Details Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background

2008-08-26

arxiv.org/abs/0808.3435v5

Class.Quant.Grav.26:055001,2009; Erratum-ibid.26:189801,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, iopart.cls. Published version with references updated

Scientific paper

10.1088/0264-9381/26/5/055001 10

It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr-(anti-)de Sitter black hole with two independent angular momenta. A first order symmetry operator that commutes with the Dirac operator is constructed in terms of a rank-three Killing-Yano tensor whose square is a second order symmetric Stackel-Killing tensor admitted by the five-dimensional Kerr-(anti-)de Sitter spacetime. We highlight the construction procedure of such a symmetry operator. In addition, the first law of black hole thermodynamics has been extended to the case that the cosmological constant can be viewed as a thermodynamical variable.

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