Nonlinear and quantum effects in analogue gravity

TL;DR

This thesis explores classical and quantum scalar fields in curved spacetime models with horizons, relating their behavior to black-hole physics and extending these analogies to various physical systems with effective Lorentz invariance.

Contribution

It provides a comprehensive analysis of nonlinear and quantum effects in analogue gravity systems, clarifying the limitations and scope of their analogy to real black-hole phenomena.

Findings

Relation between perturbations in analogue systems and black-hole physics

Limitations of the analogy in nonlinear and quantum regimes

Updated analysis of Hawking radiation in analogue models

Abstract

The present thesis deals with some properties of classical and quantum scalar fields in an inhomogeneous and/or time-dependent background, focusing on models where the latter can be described as a curved space-time with an event horizon. While naturally formulated in a gravitational context, such models extend to many physical systems with an effective Lorentz invariance at low energy. We shall see how this effective symmetry allows one to relate the behavior of perturbations in these systems to black-hole physics, what are its limitations, and in which sense results thus obtained are "analogous" to their general relativistic counterparts. The first chapter serves as a general introduction. A few notions from Einstein's theory of gravity are introduced and a derivation of Hawking radiation is sketched. The correspondence with low-energy systems is then explained through three important examples. The next four chapters each details one of the works completed during this thesis, updated and slightly reorganized to account for new developments which occurred after their publication. The other articles I contributed to are summarized in the last chapter, before the general conclusion.