In, Through and Beyond the Planck Scale

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-Nordstr\"om-like metric is self-dual in the sense of T-duality: the form of the metric is invariant under the exchange r -> a0/r where a0 is proportional to the minimum area in LQG. Of particular interest, the symmetry imposes that if an observer at infinity sees a black hole of mass m an observer in the other asymptotic infinity beyond the horizon (near r=0) sees a dual mass proportional to m_P^2/m. We then show that small LQBHs 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) m_P 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.