https://doi.org/10.1140/epjc/s10052-024-12957-6
Letter
The Bocharova–Bronnikov–Melnikov–Bekenstein black hole’s exact quasibound states and Hawking radiation
Department of Physics, Mahidol University, 272 Phraram 6 Street, 10400, Ratchathewi, Bangkok, Thailand
Received:
29
January
2024
Accepted:
21
May
2024
Published online:
12
June
2024
In this letter, we investigate behaviour of massive and massless scalar field that is represented by the covariant Klein–Gordon equation with Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) black hole background. We successfully solve analytically the governing relativistic wave equation and discover the exact quasibound states’ wave functions and energy levels of both massive and massless cases. The corresponding quasibound states have complex-valued energy 
where the real part 
can be interpreted as the scalar’s relativistic quantized energy while the imaginary part represents decay as the quasibound states tunnels through the black hole’s horizon. The Hawking radiation coming out of the BBMB black hole’s horizon is also discussed and calculated via the Damour–Ruffini method, i.e. by singling out the particle–anti-particle parts of the obtained exact scalar’s exact wave function from where, the radiation distribution function is derived and the Hawking temperature is obtained.
© The Author(s) 2024
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/.
