Black holes in full quantum gravity

Abstract

Quantum black holes have been studied extensively in quantum gravity and string theory, using various semiclassical or background-dependent approaches. We explore the possibility of studying black holes in the full non-perturbative quantum theory, without recurring to semiclassical considerations, and in the context of loop quantum gravity. We propose a definition of a quantum black hole as the collection of the quantum degrees of freedom that do not influence observables at infinity. From this definition, it follows that for an observer at infinity a black hole is described by an SU(2) intertwining operator. The dimension of the Hilbert space of such intertwiners grows exponentially with the horizon area. These considerations shed some light on the physical nature of the microstates contributing to the black hole entropy. In particular, it can be seen that the microstates being counted for the entropy have the interpretation of describing different horizon shapes. The space of black hole microstates described here is related to the one arrived at recently by Engle et al (2009, arXiv:0905.3168) and sometime ago by Smolin (1995, J. Math. Phys. 36 6417), but obtained here directly within the full quantum theory.