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.

We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress-energy preventing the formation of a singularity.

We apply the Lieb-Robinson bounds technique to find the maximum speed of interaction in a spin model with topological order whose low-energy effective theory describes light [see X.-G. Wen, Phys. Rev. B 68, 115413 (2003)]. The maximum speed of interactions is found in two dimensions is bounded from above less than √ 2e times the speed of emerging light, giving a strong indication that light is indeed the maximum speed of interactions. This result does not rely on mean field theoretic methods. In higher spatial dimensions, the Lieb-Robinson speed is conjectured to increase linearly with the dimension itself. Implications for the horizon problem in cosmology are discussed. Introduction.-The principle of locality is one of the most fundamental ideas of modern physics. It states that every physical system can be influenced only by those in its neighborhood. The concept of field is the outcome of taking this principle seriously: if object A causes a change on object B, there must be changes involving the points in between. The field is exactly what changes. In addition, if something is "happening" at all the intermediate points, then the interaction between the objects must propagate with a finite speed. Relativistic quantum mechanics is built by taking the locality principle as a central feature. In non-relativistic quantum mechanics the situation is more subtle: signals can propagate at every speed and quantum correlations are non-local in their nature. One can, in fact, send information over any finite distance in an arbitrary small time [1]. However, the amount of information that can be sent decreases exponentially with the distance if the Hamiltonian of the system is the sum of local pieces. Specifically there is an effective light cone resulting from a finite maximum speed of the interactions in quantum systems. This is the essence of the Lieb-Robinson bounds [2]. This notion have recently attracted interest in the context of quantum information theory, condensed matter physics, and the creation of topological order [1,3,4,5].