Where do Hawking quanta of a real black hole originate?

In Lorentz-invariant quantum field theory on a collapse Schwarzschild geometry of mass M, an outgoing mode of frequency $\omega \sim T_H$ at time t after collapse had, near the horizon and as measured in a frame falling freely across it, frequency $\sim \omega \exp(\kappa t)$ with $\kappa = c/(2 r_s)$, exceeding the Planck frequency after $t \sim (2 r_s/c) \ln(r_s/\ell_P)$, $\ell_P = (\hbar G/c^{3})^{1/2} \sim 1.6e-33\,\mathrm{cm}$. Identify the mechanism that supplies these modes (dispersion in a preferred frame, mode creation in a growing lattice, Lorentz-invariant nonlocality, or a full quantum gravity calculation) consistent with present bounds on Lorentz violation, and determine whether it yields $T_H = \hbar c^{3}/(8 \pi G M)$ with corrections suppressed by powers of $\ell_P/r_s$. Formulating the question within a specified ultraviolet completion is part of the problem; an answer is the mechanism plus the leading correction to $T_H$.

A derivation of the Hawking flux within a specified ultraviolet completion of gravity that shows explicitly where the outgoing modes come from and computes the first correction to $T_{\mathrm{H}}$.