Hidden Symmetries of the Dirac equation in curved spacetime

TL;DR

This paper explores the hidden symmetries of the Dirac equation in curved spacetime, linking special spacetime tensors to these symmetries, with applications to rotating higher-dimensional black holes.

Contribution

It establishes general relations between spacetime tensors and hidden symmetries for the Dirac equation and its semi-classical limit, with a specific focus on rotating higher-dimensional black holes.

Findings

Dirac equation is separable in certain black hole spacetimes

Relations between spacetime tensors and hidden symmetries are clarified

Application to higher-dimensional black holes with cosmological constant

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.