The geometric optics trace formula gives the singular support of wave trace on a compact Riemannian manifold. In the case of of a one dimensional singular manifold, that is a metric (or quantum) graph, this formula is exact and yields a crystalline measure generalizing the Poisson and related Summation Formulae.
I develop an effective theory which describes black holes with quantum
mechanical horizons that is valid at scales long compared to the
Schwarzschild radius but short compared to the lifetime of the black
hole. The formalism allows one to calculate the quantum mechanical
effects in scattering processes involving black hole asymptotic states.
The EFT Wightman functions which describe Hawking radiation in the Unruh
vacuum are not Planck suppressed and are actually enhanced relative to