Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole
Issued Date
2024-03-01
Resource Type
ISSN
14346044
eISSN
14346052
Scopus ID
2-s2.0-85186759110
Journal Title
European Physical Journal C
Volume
84
Issue
3
Rights Holder(s)
SCOPUS
Bibliographic Citation
European Physical Journal C Vol.84 No.3 (2024)
Suggested Citation
Senjaya D. Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole. European Physical Journal C Vol.84 No.3 (2024). doi:10.1140/epjc/s10052-024-12600-4 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/97529
Title
Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole
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Abstract
In this letter, we will focus on the Klein–Gordon equation with static spherically symmetric black hole solution of the Einstein–Maxwell-dilaton (EMD) theory as its 3+1 background space-time. The Klein–Gordon equation represents quasibound states of both massive and massless scalar fields which are localized in the black hole potential well. By using the covariant Klein–Gordon equation, we investigate the behaviour of both massive and massless scalars in the EMD black hole space-time. We successfully exactly solved the relativistic wave equation and are going to present the novel exact results in this letter. The exact solutions, the wave functions and the energy levels, describe the decaying nature of the relativistic scalar field bound in the curved space-time. The massive scalar quasibound state has complex-valued energy levels where the real part is the massive scalar’s energy while the imaginary part represents the decay. For the massless scalar quasibound state, pure imaginary energy levels are discovered. In this letter, by using the obtained exact scalar particle’s wave functions, we also consider the Hawking radiation of the apparent horizon of the EMD black hole that is calculated via Damour–Ruffini method. In principle, the investigation of black hole quasibound states could provide possibility for laboratory testing of effects whose nature are absolutely related with quantum effects in gravity.