Hidden Symmetries of the Dirac equation in curved spacetime
arXiv:1209.6406
Abstract
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries, both for the full Dirac equation and for its semi-classical limit, the spinning particle. A concrete application of the general results is provided by the case of rotating higher dimensional black holes with cosmological constant, which we discuss. For these metrics the Dirac equation is separable and the relation between this and hidden symmetries is explained.
Contribution written for the proceedings of the conference "Relativity and Gravitation - 100 Years after Einstein in Prague", Prague 25-29 June 2012
References in corpus (6)
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
- Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter spacetime
- Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
- Symmetries of the Dirac operator with skew-symmetric torsion
- Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds