Dynamical evaporation of quantum horizons

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We describe of the evaporation
process as driven by the dynamical evolution of the quantum gravitational
degrees of freedom resident at the horizon, as identified by the Loop Quantum
Gravity kinematics. Using a parallel with the Brownian motion, we interpret the
first law of quantum dynamical horizon in terms of a fluctuation-dissipation
relation applied to this fundamental discrete structure. In this way, the
horizon evolution is described in terms of relaxation to an equilibrium state
balanced by the excitation of Planck scale constituents of the horizon. We show
how from this setting the emergence of several conservative scenarios for the
final stage of the evaporation process can be microscopically derived. Namely,
the leakage of part of the horizon quantum geometry information prior to the
Planckian phase and the stabilization of the hole surface shrinkage forming a
massive remnant, which can eventually decay, are shown to take place.