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

TL;DR

This thesis investigates how ultraviolet Lorentz violations, modeled by nonlinear dispersion relations, affect Hawking radiation, revealing deviations, undulation phenomena, and black hole laser instabilities in analog and quantum gravity contexts.

Contribution

It provides a detailed analysis of the effects of Lorentz violation on Hawking radiation, including deviations, undulations, and black hole laser instabilities, advancing understanding in analog gravity and quantum gravity models.

Findings

Deviations from standard Hawking radiation due to dispersion.

Emergence of undulation phenomena in white hole flows and massive fields.

Identification of black hole laser instability with exponential flux growth.

Abstract

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.