Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Abstract

We study a charged and massive scalar field in the background of the Nutku-Ghezelbash-Kumar metric which is obtained by the addition of a time coordinate to the Nutku helicoid metric in a non-trivial way. The angular part of the Klein-Gordon equation can be written as a double confluent Heun equation. The radial equation cannot be solved in terms of a known function in its general form. However, in some special cases, the radial equation can also be written explicitly as a double confluent Heun equation. We study the full radial equation numerically and observe that the electromagnetic field parameter defines an effective cut-off on the range of the radial coordinate. Finally, we obtain a quasi-exact solution with an approximation.

14 pages, 8 figures. Matches the published version

References in corpus (6)

• Heun equation, Teukolsky equation, and type-D metrics
• Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
• Dirac Equation in the Background of the Nutku Helicoid Metric
• An Analysis of the Wave Equation for the $U(1{)}^2$ Gauged Supergravity Black Hole
• Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution
• M-Branes on Minimal Surfaces

Cited by in corpus (1)

• Analysis of scalar fields with series convolution