Tunnelling radiation and the microstates of a black hole influenced by the Lorentz invariance violation

¹ Physics and Space College, China West Normal University - Nanchong, 637000, PRC
² Department of Physics, Si Chuan MinZu College - Kangding, 626001, PRC

^(a) gpliphys@yeah.net (corresponding author)
^(b) binbchen@126.com

Received: 17 April 2020
Accepted: 31 August 2020

Abstract

In this paper, we have employed the second-order Lorentz invariance violation (LIV) to carefully investigate the effect of quantum gravity on the Hawking radiation of the Dirac particle via tunneling from the Kerr black hole. Firstly, it turns out that the Hawking temperature is not only related to the angular momentum and mass of the black hole, but related to the energy and mass of the emitted particle. In particular, we find that the effective temperature is bigger and bigger with the increase of the energy ω, the angular momentum j and the LIV parameter l_p, but is smaller and smaller with the increase of the black hole mass M. Also, it further shows that, although quantum gravity speeds up the black-hole evaporation, it will not evaporate completely, instead a remaining mass, temperature and entropy are left. Finally, through a careful count of the number of the microstates taken away by the black-hole radiation, the initial and remaining number of microstates for the Schwarzschild black hole are presented with the inclusion of the LIV-induced quantum gravity effects.