  In this thesis, we study several features of Hawking radiation in the
presence of ultraviolet Lorentz violations. These violations are implemented by
a modified dispersion relation that becomes nonlinear at short wavelengths. The
motivations of this work arise on the one hand from the developing field of
analog gravity, where we aim at measuring the Hawking effect in fluid flows
that mimic black hole space-times, and on the other hand from the possibility
that quantum gravity effects might be approximately modeled by a modified
dispersion relation. We develop several studies on various aspects of the
problem. First we obtain precise characterizations about the deviations from
the Hawking result of black hole radiation, which are induced by dispersion.
Second, we study the emergence, both in white hole flows or for massive fields,
of a macroscopic standing wave, spontaneously produced from the Hawking effect,
and known as `undulation'. Third, we describe in detail an instability named
black hole laser, which arises in the presence of two horizons, where Hawking
radiation is self-amplified and induces an exponentially growing in time
emitted flux.
