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


Birkandan T. , HORTACSU M.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.40, no.5, pp.1105-1116, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 5
  • Publication Date: 2007
  • Doi Number: 10.1088/1751-8113/40/5/016
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
  • Page Numbers: pp.1105-1116

Abstract

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. As a new example we find that while the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime 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.