Mathematical model of Diraka particles emission from the surface of an elliptical black hole

According to the general theory of relativity, a black hole is defined as a region of space-time with superstrong gravitational effects, and even photons cannot escape from it, with their limiting velocities in vacuum. So in classical relativity theory we can say with certainty that a black hole is a "dead" thermodynamic object. However, using the theory of quantum mechanics, Hawking showed that a black hole can emit particles. This paper presents a mathematical model for calculating the temperature of an elliptical black hole when emitting Dirac particles. Using the complex approach, the emission can be described as a process of radiation on tunnel structures. From the relation between the probability of particle output and the black body radiation spectrum for fermionic particles the elliptical black hole temperature can be derived and it is proved that it depends on the azimuthal angle. This result also showed the absence of thermodynamic equilibrium of the elliptic black hole surface.