Exact massless spinor quasibound states of Schwarzschild black hole

In this work, we investigate the behaviour of massless spin 12 field by working out the Dirac equation in a curved static spherically symmetric Schwarzschild space-time. Detailed derivation of novel exact massive and massless scalar quasibound state in Schwarzschild black hole background is presented in this work. After decoupling the Dirac equation, we successfully solve both of the angular and radial parts, respectively in terms of spin weighted Spherical Harmonics and Confluent Heun functions. With the exact radial wave solution in hand, applying its polynomial condition leads to the discovery of the the quantized energy levels expression. We found that the massless spinor field around the Schwarzschild black hole has complex valued energy levels, in contrast to the purely imaginary for a massless boson around the same black hole. In the last section, the Hawking radiation distribution function is derived via Damour-Ruffini method and the Hawking temperature is obtained.