https://doi.org/10.1140/epjc/s10052-025-15128-3
Regular Article - Theoretical Physics
Revisiting Kerr–Newman black hole’s charged scalar cloud: flux balance
Department of Physics, Faculty of Science, Mahidol University, Bangkok, Thailand
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
18
October
2025
Accepted:
26
November
2025
Published online:
5
December
2025
Abstract
In the present study, we investigate the quasibound states and scalar cloud of relativistic charged scalar fields bound to a Kerr–Newman black hole. We present the exact eigensolutions of the governing Klein–Gordon equation with non-minimal coupling in the black hole background. By imposing boundary conditions on the quasibound states, we are able to find the exact complex quasibound state frequencies of the corresponding radial wave functions in terms of the confluent Heun polynomial. The quantization formula obtained here allows us to determine the exact resonance frequency of a charged scalar cloud, thereby revisiting and extending the earlier result derived through the asymptotic matching approach. Our analysis shows that a stationary configuration can exist only when the charge coupling satisfies 
. In this case, the scalar cloud remains stationary due to a flux balance: an outgoing flux from the Cauchy horizon compensates for the ingoing particle flux at the event horizon. This mechanism distinguishes scalar clouds from ordinary quasibound states, where such a compensating flux is absent.
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-025-15274-8.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
