  Using a recently developed quantization of spherically symmetric gravity
coupled to a scalar field, we give a construction of null expansion operators
that allow a definition of general, fully dynamical quantum black holes. These
operators capture the intuitive idea that classical black holes are defined by
the presence of trapped surfaces, that is surfaces from which light cannot
escape outward. They thus provide a mechanism for classifying quantum states of
the system into those that describe quantum black holes and those that do not.
We find that quantum horizons fluctuate, confirming long-held heuristic
expectations. We also give explicit examples of quantum black hole states. The
work sets a framework for addressing the puzzles of black hole physics in a
fully quantized dynamical setting.
