Special functions and perturbations of black holes.

*(English)* Zbl 1097.83520
Dunkl, Charles (ed.) et al., Special functions. Proceedings of the international workshop on special functions – asymptotics, harmonic analysis and mathematical physics, Hong Kong, China, June 21–25, 1999. Singapore: World Scientific (ISBN 981-02-4393-6/hbk). 140-151 (2000).

Summary: It is known that perturbations of black holes for which not all of the defining parameters (i.e., mass, angular momentum and charge) are nonzero can be calculated explicitly. In the case of zero charge these perturbations can computed using Debye potentials, which are special functions of confluent Heun type. There is however no scheme for the corresponding solution of the perturbation problem for a massive charged rotating black hole. In this paper we discuss how this problem may be solved using the idea of a symmetry operator and an integral equation formulation. In addition, we give a summary of the geometric features of the black hole spacetimes which account for some of their remarkable properties.

##### MSC:

83C57 | Black holes |

33C90 | Applications of hypergeometric functions |

34B60 | Applications of theory of BVP for ODE |