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In this thesis, we study several features of Hawking radiation in thepresence of ultraviolet Lorentz violations. These violations are implemented bya modified dispersion relation that becomes nonlinear at short wavelengths. Themotivations of this work arise on the one hand from the developing field ofanalog gravity, where we aim at measuring the Hawking effect in fluid flowsthat mimic black hole space-times, and on the other hand from the possibilitythat quantum gravity effects might be approximately modeled by a modifieddispersion relation. We develop several studies on various aspects of theproblem. First we obtain precise characterizations about the deviations fromthe 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 namedblack hole laser, which arises in the presence of two horizons, where Hawkingradiation is self-amplified and induces an exponentially growing in timeemitted flux.

Stability properties of Hawking radiation in the presence of ultraviolet violation of local Lorentz invariance