Exact massive and massless scalar quasibound states around a charged Lense-Thirring black hole

Abstract

In this work, we present a detailed derivation of novel exact massive and massless scalar quasibound state in a slowly rotating black hole background. We successfully solve the governing covariant Klein-Gordon equation and discover the exact radial solutions in terms of the Confluent Heun functions. With the exact radial wave solution in hand, applying its polynomial condition leads to the discovery of the quantized energy levels expression that depends on the black hole's mass M, spin a, charge rQ and also the magnetic and main quantum number (mℓ,n). A massive scalar field around the black hole has complex valued energy levels while massless particle has purely imaginary energy levels. Further investigation by considering small black hole limit and zero charge, the previously published results are recovered. In the last section, the Hawking radiation is investigated and applying the Damour-Ruffini method, the Hawking temperature is obtained out of the radiation distribution function.