The Bocharova–Bronnikov–Melnikov–Bekenstein black hole’s exact quasibound states and Hawking radiation

Abstract

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 E=ER+iEI where the real part ER 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.