Thermodynamics and phases in quantum gravity

We give an approach for studying quantum gravity effects on black hole thermodynamics. This combines a quantum framework for gravitational collapse with quasi-local definitions of energy and surface gravity. Our arguments suggest that (i) the specific heat of a black hole becomes positive after a phase transition near the Planck scale,(ii) its entropy acquires a logarithmic correction, and (iii) the mass loss rate is modified such that Hawking radiation stops near the Planck scale. These results are due essentially to a realization of fundamental discreteness in quantum gravity, and are in this sense potentially theory independent. The first law of black hole mechanics is a result concerning a subspace of the solution space of Einstein’s equations parametrized by a black hole’s mass, charge, and angular momentum. Perturbations of these parameters are related, and this comprises the first law [1]. For the simplest Schwarzschild black hole the law is