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General Relativity and Quantum Cosmology

arXiv:2204.10627 (gr-qc)
[Submitted on 22 Apr 2022 (v1), last revised 27 Jul 2023 (this version, v2)]

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

Authors:Tolga Birkandan
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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.
Comments: 14 pages, 8 figures. Matches the published version
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:2204.10627 [gr-qc]
  (or arXiv:2204.10627v2 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.2204.10627
Journal reference: Gen Relativ Gravit 55, 88 (2023)
Related DOI: https://doi.org/10.1007/s10714-023-03134-3

Submission history

From: Tolga Birkandan [view email]
[v1] Fri, 22 Apr 2022 10:44:53 UTC (171 KB)
[v2] Thu, 27 Jul 2023 14:23:44 UTC (234 KB)
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