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Examples of Heun and Mathieu functions as solutions of wave equationsin curved spaces

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
T. Birkandan  and
M. Horta
T. Birkandan
Affiliation:
Istanbul Technical University, Department of Physics, 34469 Maslak, Istanbul, Turkey
M. Horta
Affiliation:
Istanbul Technical University, Department of Physics, 34469 Maslak, Istanbul, Turkey
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Abstract

We give examples of where the Heun function exists as solutions ofwave equations encountered in general relativity. While the Diracequation written in the background of Nutku helicoid metric yieldsMathieu functions as its solutions in four spacetime dimensions,the trivial generalization to five dimensions results in thedouble confluent Heun function. We reduce this solution to theMathieu function with some transformations. We must applyAtiyah-Patodi-Singer spectral boundary conditions to this systemsince the metric has a singularity at the origin.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles, ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 265 - 268
Copyright
© EAS, EDP Sciences, 2008

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References

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