Heun and Mathieu functions as solutions of the Dirac equation

Details Heun and Mathieu functions as solutions of the Dirac equation Heun and Mathieu functions as solutions of the Dirac equation

2007-10-23

arxiv.org/abs/0710.4243v1

EAS Publ.Ser.30:265,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, Prepared for the Spanish Relativity Meeting (ERE 2007), Tenerife, Spain, 10-14 Sep 2007

Scientific paper

10.1051/eas:0830041

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.

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