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

摘要

We give examples where the Heun function exists in general relativity. Itturns out that while a wave equation written in the background of certainmetric yields Mathieu functions as its solutions in four space-time dimensions,the trivial generalization to five dimensions results in the double confluentHeun function. We reduce this solution to the Mathieu function with sometransformations.