  Using the earlier developed classical Hamiltonian framework as the point of
departure, we carry out a non-perturbative quantization of the sector of
general relativity, coupled to matter, admitting non-rotating isolated horizons
as inner boundaries. The emphasis is on the quantum geometry of the horizon.
Polymer excitations of the bulk quantum geometry pierce the horizon endowing it
with area. The intrinsic geometry of the horizon is then described by the
quantum Chern-Simons theory of a U(1) connection on a punctured 2-sphere, the
horizon. Subtle mathematical features of the quantum Chern-Simons theory turn
out to be important for the existence of a coherent quantum theory of the
horizon geometry. Heuristically, the intrinsic geometry is flat everywhere
except at the punctures. The distributional curvature of the U(1) connection at
the punctures gives rise to quantized deficit angles which account for the
overall curvature. For macroscopic black holes, the logarithm of the number of
these horizon microstates is proportional to the area, irrespective of the
values of (non-gravitational) charges. Thus, the black hole entropy can be
accounted for entirely by the quantum states of the horizon geometry. Our
analysis is applicable to all non-rotating black holes, including the
astrophysically interesting ones which are very far from extremality.
Furthermore, cosmological horizons (to which statistical mechanical
considerations are known to apply) are naturally incorporated. An effort has
been made to make the paper self-contained by including short reviews of the
background material.
