Exact analytical quasibound states of a scalar particle around a slowly rotating black hole

Abstract

In this work, behaviour of massive and massless scalar particle around a slowly rotating black hole in 3+1 dimension is investigated. Exact solutions of the Klein-Gordon equation, i.e. the wave functions and energy levels are discovered. The quasibound state has complex-valued energy levels E=ER+iEI where the real part ER is directly related to the particle's energy while the imaginary part represents a decay. Using the obtained exact wave solutions near the exterior horizon of the black hole, the Hawking radiation is discussed.