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

2006/07/31 by T. Birkandan, Tolga Birkandan, M. Hortaçsu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #gr-qc #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/40/5/016

published as J.Phys.A40:1105-1116,2007; J.Phys.A40:11203,2007 · 18 pages, Minor improvements, references added

openalex publication_date 2007/01/17 · arxiv created 2007/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On reducing the Heun equation to the hypergeometric equation
• Gravitational instantons, confocal quadrics and separability of the Schr dinger and Hamilton–Jacobi equations
• An Approach to Gravitational Radiation by a Method of Spin Coefficients

Cited by

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