Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory
Abstract
The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetič and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Stäckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.
- Publication:
-
Physical Review D
- Pub Date:
- August 2009
- DOI:
- 10.1103/PhysRevD.80.044037
- arXiv:
- arXiv:0902.2823
- Bibcode:
- 2009PhRvD..80d4037W
- Keywords:
-
- 04.50.Gh;
- 04.62.+v;
- 04.70.Bw;
- 11.10.Kk;
- Higher-dimensional black holes black strings and related objects;
- Quantum field theory in curved spacetime;
- Classical black holes;
- Field theories in dimensions other than four;
- High Energy Physics - Theory;
- Astrophysics - High Energy Astrophysical Phenomena;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Phenomenology;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 20 pages, accompanied paper to arXiv:0807.2114 [hep-th] and arXiv:0808.3435 [hep-th]. Published version