  We construct a diffeormorphism invariant operator that is sensitive to how
far we are from the black hole horizon. Its expectation value blows up on the
horizon and it is small away from the horizon. Using this operator, we propose
a non-standard effective action that, we argue, captures some of the relevant
physics of quantum black holes, including the absence of the horizon at the
full quantum level. With the help of a toy version of this effective action, we
speculate on a possible connection between UV/IR mixing and the cosmological
constant problem.
