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arXiv · 2204.10627

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

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.

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Tolga Birkandan. 2022-04-22. Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field. https://doi.org/10.1007/s10714-023-03134-3

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