Self-dual Black Holes in LQG: 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-Nordstrom-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 at "r" close to infinity sees a black hole of mass "m" an observer in the other asymptotic infinity beyond the horizon (at "r" close to "0") sees a dual mass "mp/m" ("mp" is the Planck mass). 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.

18 pages, 32 figures. Extra Plot, Improved Numerical Results and Corrected typos

References in corpus (25)

• Quantum Gravity at a Lifshitz Point
• LQG vertex with finite Immirzi parameter
• The loop-quantum-gravity vertex-amplitude
• Quantum Tunneling and Back Reaction
• Noncommutative Black Hole Thermodynamics
• Loop Quantum Dynamics of the Schwarzschild Interior
• Flipped spinfoam vertex and loop gravity
• Fermion Tunneling Beyond Semiclassical Approximation
• Black holes in loop quantum gravity: the complete space-time
• Quantum Tunneling and Trace Anomaly
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Loop Quantum Gravity: An Inside View
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Loop quantization of spherically symmetric midi-superspaces
• The length operator in Loop Quantum Gravity
• Black hole interior from loop quantum gravity
• Noncommutative Schwarzschild Black Hole and Area Law
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Thermodynamics of regular black hole
• Path integral representation of spin foam models of 4d gravity
• Inflationary universe in loop quantum cosmology
• Quantum Cooling Evaporation Process in Regular Black Holes
• Gravitational collapse in loop quantum gravity
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Semiclassical regime of Regge calculus and spin foams