  We study the Hawking radiation in field theories which break Lorentz
invariance via dissipative effects above a certain energy scale. We assume that
the additional degrees of freedom which cause dissipation are Gaussian and
freely falling. The asymptotic spectrum and the correlations are extracted from
the anticommutator of the radiation field. The singular behavior of the Green
function found for relativistic fields as one point crosses the horizon is
completely suppressed by dissipation. Yet, when the dissipative frequency scale
is much larger than the surface gravity of the black hole, we show that the
asymptotic observables acquire their standard (relativistic) vacuum expectation
values. We explicitly compute the effects of dissipation on the spectrum and on
the nonseparable character of the correlations when varying the dissipative
scale, the extension of the near-horizon geometry, and the temperature of the
environment.
