  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,
Noui and Perez, and sometime ago by Smolin, but obtained here directly within
the full quantum theory.
