Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole

Abstract

In curved space-time, the Hamilton-Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics. In this paper, starting from the Dirac equation of spin 1/2 fermions and the Rarita-Schwinger equation of spin 3/2 fermions, respectively, we derive a Hamilton-Jacobi equation for the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling of a charged spherically symmetric Kinnersly black hole is investigated by using the Hamilton-Jacobi equation. The result shows that the Hamilton-Jacobi equation is helpful to understand the thermodynamic properties and the radiation characteristics of a black hole.

Massless fermions on static general prolate metrics and their Heun solutions

“…One may look for a polynomial form of the Heun functions in (22), by imposing that the third parameter is satisfying the necessary (not sufficient) condition α = −n, with n a positive integer and q has one of a finite number of characteristic values, which fixes the value of λ. This can be done for α ′ in (24), leading to the quantized imaginary spectrum…”