# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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