Quantum horizon and thermodynamics of black hole

Abstract

A semi-classical reasoning leads to the non-commutativity of space and time coordinates near the horizon of static non-extreme black hole, and renders the classical horizon spreading to {\it Quantum Horizon} . In terms of the background metric of the black hole with the {\it Quantum Horizon}, a quantum field theory in curved space without ultraviolet divergency near the horizon is formulated. In this formulism, the black hole thermodynamics is reproduced correctly without both ambiguity and additional hypothesis in the deriving the hole's Hawking radiations and entropies, and a new interesting prediction on the number of radiative field modes $N$ is provided. Specifically, the main results are follows: 1, Hawking radiations rightly emerge as an effect of quantum tunneling through the quantum horizon, and hence the ambiguities due to going across the singularity on the classical horizon were got rid of; 2, 't Hooft's brick wall thickness hypothesis and the boundary condition imposed for the field considered in his brick wall model were got rid of also, and related physics has been interpreted; 3, The present theory is parameter free. So, the theory has power to predict the multiplicity $N$ of radiative field modes according to the requirement of normalization of Hawking-Bekenstein entropy. It has been found that $N\simeq 162$, which is just in good agreement with one in the Minimal Super-symmetric Standard Model. The studies in this paper represent an attempt to reveal some physics near the horizon at Planck scale. This paper serves a brief review on the author's works on this subject.