Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-03T09:07:58.524Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aliev, A.N., Hortaçsu, M., Kalaycı, J., & Nutku, Y., 1999, Class. Quant. Grav., 16, 631 CrossRef
Aliev, A.N., & Nutku, Y., 1999, Class. Quan. Grav., 16, 189 CrossRef
Atiyah, M.F., Patodi, V.K., & Singer, I.M., 1975, Math. Proc. Cambridge Phil. Soc., 77, 43; 78, 405 CrossRef
Birkandan, T., & Hortaçsu, M., 2007, J. Phys. A, 40, 1105 CrossRef
Birkandan, T., & Hortaçsu, M., 2007, J. Math. Phys., 48, 092301 CrossRef
Chaos-Cador, L., & Ley-Koo, E., 2002, Rev. Mex. Fis., 48, 67
Fiziev, P.P., 2006, Class. Quant. Grav., 23, 2447 CrossRef
Hortaçsu, M., 1983, Lettere Nuovo Cim., 36, 109 CrossRef
Hortaçsu, M., Rothe, K.D., & Schroer, B., 1980, Nucl. Phys. B, 171, 530 CrossRef
Nutku, Y., 1996, Phys. Rev. Lett., 77, 4702 CrossRef
Ronveaux, A., 1995, Heun's Differential Equations (ed. Oxford University Press)
Siopsis, G., 2005, Nucl. Phys. B, 715, 483, [hep-th/0407157] CrossRef
Sucu, Y., Ünal, N., 2004, Class. Quant. Grav., 21, 1443 CrossRef