Exact analytical quasibound states of a scalar particle around a Reissner-Nordström black hole

Abstract

In this paper, we investigate behavior of massive and massless scalar particle around a static spherically symmetric charged black hole—so called Reissner-Nordström black hole in 3+1 dimension. We successfully discover a novel exact analytical quasibound states' wave functions and energy levels by solving the covariant Klein-Gordon wave equation. The quasibound state has complex-valued energy E=ER+iEI where the real part ER can be interpreted as the scalar particle's energy while the imaginary part represents the decay. We also discuss the Hawking radiation from the apparent horizon of Reissner-Nordström black hole which can be calculated using the scalar particle's wave function. In principle, this study could provide the possibility for laboratory testing of effects whose nature is absolutely related with quantum effects in gravity.