An Improvement for Quantum Tunneling Radiation of Fermions in a Stationary Kerr-Newman Black Hole Spacetime

TL;DR

This paper introduces a modified approach to quantum tunneling radiation of fermions in Kerr-Newman black holes by incorporating Lorentz Invariance Violation, revealing effects on Hawking temperature and entropy.

Contribution

It proposes a new method using a Lorentz-violating Dirac equation to analyze fermion tunneling in curved spacetime, specifically applied to Kerr-Newman black holes.

Findings

Hawking temperature increases with LIV parameters

Black hole entropy decreases due to LIV effects

Modified fermion equations affect black hole thermodynamics

Abstract

By introducing a specific etheric-like vector in the Dirac equation with Lorentz Invariance Violation (LIV) in the curved spacetime, an improved method for quantum tunneling radiation of fermions is proposed. As an example, we apply this new method to a charged axisymmetric Kerr-Newman black hole. Firstly, considering LIV theory, we derive a modified dynamical equation of fermion with spin 1/2 in the Kerr-Newman black hole spacetime. Then we solve the equation and find the increase or decrease of black hole's Hawking temperature and entropy are related to constants $a$ and $c$ of the Dirac equation with LIV in the curved spacetime. As $c$ is positive, the new Hawking temperature is about $ \frac{\sqrt{1+2a+2cmk_r^2}}{\sqrt{1+2a}}$ times higher than that without modification, but the entropy will decrease. We also make a brief discussion for the case of high spin fermions.