Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces

Details Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces

2006-07-25

arxiv.org/abs/gr-qc/0607108v3

J.Phys.A40:1105-1116,2007; J.Phys.A40:11203,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, Minor improvements, references added

Scientific paper

10.1088/1751-8113/40/5/016 10.10

We give examples where the Heun function exists in general relativity. It turns out that while a wave equation written in the background of certain metric yields Mathieu functions as its solutions in four space-time dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations.

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