2007/10/23 by T. Birkandan, M. Hortacsu, M. Horta
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Quantum Mechanics and Non-Hermitian Physics #gr-qc
paper · pdf · doi:10.1051/eas:0830041
published as EAS Publ.Ser.30:265,2008 · 5 pages, Prepared for the Spanish Relativity Meeting (ERE 2007), Tenerife, Spain, 10-14 Sep 2007
arxiv created 2007/10/23 · openalex publication_date 2008/01/01 · arxiv updated 2011/08/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. 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. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.