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

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 obtained in loop quantum gravity is invariant under the exchange r→a₀/r where a₀ is proportional to the minimum area in loop quantum gravity 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. Ultralight LQBHs created shortly after the big bang would now have a mass of approximately 10^-5mP and emit radiation with a typical energy of about 10¹³--10¹⁴ 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 ultralight black holes would be compatible with the observed rate of the Auger detector.