Self-dual black holes in loop quantum gravity: Theory and phenomenology

Abstract

In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordström-like metric is self-dual in the sense of T-duality: the form of the metric obtained in Loop quantum Gravity (LQG) is invariant under the exchange r → a0/r where a0 is proportional to the minimum area in LQG and r is the standard Schwarzschild radial coordinate at asymptotic infinity. Of particular interest, the symmetry imposes that if an observer in r → +∞ sees a black hole of mass m an observer in the other asymptotic infinity beyond the horizon (at r ≈ 0) sees a dual mass mP /m. We then show that small LQBH are stable and could be a component of dark matter. Ultra-light LQBHs created shortly after the Big Bang would now have a mass of approximately 10 −5 mP and emit radiation with a typical energy of about 10 13 − 10 14 eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultra light black holes would be compatible with the observed rate of the Auger detector.

Quantum Tunneling Radiation from Loop Quantum Black Holes and the Information Loss Paradox

“…The temperature and entropy of this kind of black hole are calculated by the use of the tunneling method. These first results presented in [38] replicate those found in the references [40][41][42], where other methods have been used. In this way, it can be demonstrated that the quantum tunneling formalism can be successfully applied to address the thermodynamics of LQBHs, opening a path for a whole range of applications.…”

“…which coincides with the former Expression (11) found out in the references [40][41][42]. From the expression for LQBH temperature, one obtains for the entropy:…”

“…We have shown that the results obtained in the references [40][41][42] for the LQBH temperature and entropy can be reproduced by the use of the tunneling method, in a way that such a method can be, in fact, reliably applied in order to address LQBH thermodynamics. We have also presented the results related with the inclusion of back reaction effects in the description of the LQBH evaporation process.…”

“…In order to do this, we shall investigate the thermodynamic properties of Loop Quantum Black Holes [39,40], which correspond to a quantum corrected black hole solution that appears in the context of LQG. The temperature and entropy of this kind of black hole are calculated by the use of the tunneling method.…”

On the holographic basis of loop quantum cosmology

“…In this way, a Loop Quantum Black Hole (LQBH), also called self-dual black hole, consists in a quantum corrected Schwarzschild black hole that appears from a simplified model of LQG by the use of semiclassical tools in the minisuperspace quantization approach [40][41][42][43].…”