The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation
Issued Date
2024-04-01
Resource Type
ISSN
14346044
eISSN
14346052
Scopus ID
2-s2.0-85191193581
Journal Title
European Physical Journal C
Volume
84
Issue
4
Rights Holder(s)
SCOPUS
Bibliographic Citation
European Physical Journal C Vol.84 No.4 (2024)
Suggested Citation
Senjaya D. The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation. European Physical Journal C Vol.84 No.4 (2024). doi:10.1140/epjc/s10052-024-12794-7 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/98171
Title
The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation
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Abstract
In this letter, we will focus on the Klein–Gordon equation with rotating axially symmetric black hole solution of the Einstein–Bumblebee theory, so called the Kerr–Bumblebee black hole, as its 3 + 1 background space-time. We start with constructing the covariant Klein–Gordon equation component by component and with the help of the ansatz of separation of variables, we successfully separate the polar part and found the exact solution in terms of Spheroidal Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that is resulted in a complex-valued energy levels expression for a massive scalar field, where the real part is the scalar particle’s energy while the imaginary part represents the quasibound stats’s decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe the decaying nature of the relativistic scalar field bound in the curved Kerr–Bumblebee space-time. We also investigate the Hawking radiation of the Kerr–Bumblebee black hole’s apparent horizon via the Damour–Ruffini method by making use the obtained exact scalar’s wave functions. The radiation distribution function and the Hawking temperature are successfully obtained.