Evaporating loop quantum black hole

In this paper we obtain the black hole metric from a semiclassical analysis of loop quantum black hole. Our solution and the Schwarzschild one tend to match well at large distances from Planck region. In r = 0 the semiclassical metric is regular and singularity free in contrast to the classical one. By using the new metric we calculate the Hawking temperature and the entropy. For the entropy we obtain the logarithmic correction to the classical area law. Finally we study the mass evaporation process and we show the mass and temperature tend to zero at infinitive time. Introduction Quantum gravity is the theory by which we tray to reconcile general relativity and quantum mechanics. In general relativity the space-time is dynamical then it is not possible to study other interactions on a fixed background because the background itself is a dynamical field. The theory called “loop quantum gravity” (LQG) [1] is the most widespread nowadays. This is one of the non perturbative and background independent approaches to quantum gravity (another non perturbative approach to quantum gravity is called “asymptotic safety quantum gravity” [2]). Loop quantum gravity is a quantum geometric fundamental theory that reconciles general relativity and quantum mechanics at the Planck scale. The main problem nowadays is to connect this fundamental theory with standard model of particle physics and in particular with the effective quantum field theory. In the last two years great progresses has been done to connect (LQG) with the low energy physics by the general boundary approach [3], [4]. Using this formalism it has been possible to calculate the graviton propagator in four [5], [6] and three dimensions [7], [8]. In three dimensions it has been showed that a noncommuative field theory can be obtained from spinfoam models [9]. Similar efforts in four dimension are going in progress [10]. Early universe and black holes are other interesting places for testing the validity of LQG. In the past years applications of LQG ideas to minisuperspace models lead to some interesting results in those fields. In particular it has been showed in cosmology [11], [12] and recently in black hole physics [13], [14], [15], [16] that it is possible to solve the cosmological singularity problem and the black hole singularity problem by using tools and ideas developed in full loop quantum gravity theory. ∗Electronic address: [email protected] or [email protected]