Antonin Coutant

Black hole radiation with short distance dispersion, an analytical S-matrix approach

Local and non-local properties of Hawking radiation in the presence of short distance dispersion are computed using connection formulae. The robustness of the spectrum and that of the two-point function are explained by showing that the leading deviations from the relativistic expressions decrease with the inverse of the spatial extension of the near horizon region. This region corresponds to a portion of de Sitter space with a preferred frame. We show that the phases of the Bogoliubov coecients are relevant for the two-point function in black and white holes, and also for the black hole laser eect. We also present an unexpected relation between the spectra obtained with sub and with superluminal dispersion and we apply our formalism to massive elds. Our predictions are validated by numerical analysis.

Rotational superradiant scattering in a vortex flow

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), 09210170 Santo André, São Paulo, Brazil Department of Civil Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, Canada V6T 1Z4 School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK.

Hawking radiation of massive modes and undulations

We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in the supersonic region, which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what was recently found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime.

Detecting Rotational Superradiance in Fluid Laboratories

Rotational superradiance was predicted theoretically decades ago, and is chiefly responsible for a number of important effects and phenomenology in black-hole physics. However, rotational superradiance has never been observed experimentally. Here, with the aim of probing superradiance in the lab, we investigate the behavior of sound and surface waves in fluids resting in a circular basin at the center of which a rotating cylinder is placed. We show that with a suitable choice for the material of the cylinder, surface and sound waves are amplified. Two types of instabilities are studied: one sets in whenever superradiant modes are confined near the rotating cylinder and the other, which does not rely on confinement, corresponds to a local excitation of the cylinder. Our findings are experimentally testable in existing fluid laboratories and, hence, offer experimental exploration and comparison of dynamical instabilities arising from rapidly rotating boundary layers in astrophysical as well as in fluid dynamical systems.

The imprint of the analogue Hawking effect in subcritical flows

We study the propagation of low-frequency shallow water waves on a one-dimensional flow of varying depth. When taking into account dispersive effects, the linear propagation of long-wavelength modes on uneven bottoms excites new solutions of the dispersion relation which possess a much shorter wavelength. The peculiarity is that one of these new solutions has a negative energy. When the flow becomes supercritical, this mode has been shown to be responsible for the (classical) analog of the Hawking effect. For subcritical flows, the production of this mode has been observed numerically and experimentally, but the precise physics governing the scattering remained unclear. In this work, we provide an analytic treatment of this effect in subcritical flows. We analyze the scattering of low-frequency waves using a new perturbative series, derived from a generalization of the Bremmer series. We show that the production of short-wavelength modes is governed by a complex value of the position: a complex turning point. Using this method, we investigate various flow profiles and derive the main characteristics of the induced spectrum.

Impossibility of superluminal travel in Lorentz violating theories

Warp drives are space-times allowing for superluminal travel. However, they are quantum mechanically unstable because they produce a Hawking-like radiation which is blue shifted at their front wall without any bound. We re-examine this instability when local Lorentz invariance is violated at ultra high energy by dispersion, as in some theories of quantum gravity. Interestingly, even though the ultraviolet divergence is now regulated, warp drives are still unstable. Moreover the type of instability is different whether one uses a subluminal or a superluminal dispersion relation. In the first case, a black-hole laser yields an exponential amplification of the emitted flux whereas, in the second, infrared effects produce a linear growth of that flux. These results suggest that chronology could still be protected when violating Lorentz invariance.

Waves on a vortex: rays, rings and resonances

We study the scattering of surface water waves with irrotational draining vortices. At small depth, this system is a mathematical analogue of a rotating black hole and can be used to mimic some of its peculiar phenomenon. Using ray-tracing methods, we exhibit the existence of unstable orbits around vortices at arbitrary depth. These orbits are the analogue of the light rings of a black hole. We show that these orbits come in pairs, one co-rotating and one counter-rotating, at a critical radius that varies with the frequency. We derived an explicit formula for this radius in the deep water regime. Our method is validated by comparison with recent experimental data from a wavetank experiment. We finally argue that these rings will generate a discrete set of damped resonances that we characterize and that could possibly be observed in future experiments.

Low-frequency analogue Hawking radiation: the Korteweg–de Vries model

We derive analytic expressions for the low-frequency properties of the analogue Hawking radiation in a general weak-dispersive medium. A thermal low-frequency part of the spectrum is expected even when dispersive effects become significant. We consider the two most common class of weak-dispersive media and investigate all possible anomalous scattering processes due inhomogeneous background flows. We first argue that under minimal assumptions, the scattering processes in near-critical flows are well described by a linearized Korteweg-de Vries equation. Within our theoretical model greybody factors are neglected, that is, the mode co-moving with the flow decouples from the other ones. We also exhibit a flow example with an exact expression for the effective temperature. We see that this temperature coincides with the Hawking one only when the dispersive length scale is much smaller than the flow gradient scale. We apply the same method in inhomogeneous flows without an analogue horizon. In this case, the spectrum coefficients decrease with decreasing frequencies. Our findings are in agreement with previous numerical works, generalizing their findings to arbitrary ow profiles. Our analytical expressions provide estimates to guide ongoing experimental efforts.

Low-frequency analogue Hawking radiation: The Bogoliubov-de Gennes model

We analytically study the low-frequency properties of the analogue Hawking effect in Bose-Einstein condensates. We show that in one-dimensional flows displaying an analogue horizon, the Hawking effect is dominant in the low-frequency regime. This happens despite non vanishing greybody factors, that is, the coupling of the Hawking mode and its partner to the mode propagating with the flow. To show this, we obtained analytical expressions for the scattering coefficients, in general flows and taking into account the full Bogoliubov dispersion relation. We discuss the obtained expressions for the greybody factors. In particular, we show that they can be significantly decreased if the flow obeys a conformal coupling condition. We argue that in the presence of a small but non-zero temperature, reducing greybody factors greatly facilitates the observation of entanglement, that is, establishing that the state of the Hawking mode and its partner is non-separable.

Dynamical instabilities and quasi-normal modes, a spectral analysis with applications to black-hole physics

Black hole dynamical instabilities have been mostly studied in specific models. We here study the general properties of the complex-frequency modes responsible for such instabilities, guided by the example of a charged scalar field in an electrostatic potential. We show that these modes are square integrable, have a vanishing conserved norm, and appear in mode doublets or quartets. We also study how they appear in the spectrum and how their complex frequencies subsequently evolve when varying some external parameter. When working on an infinite domain, they appear from the reservoir of quasi-normal modes obeying outgoing boundary conditions. This is illustrated by generalizing, in a non-positive definite Krein space, a solvable model (Friedrichs model) which originally describes the appearance of a resonance when coupling an isolated system to a mode continuum. In a finite spatial domain instead, they arise from the fusion of two real frequency modes with opposite norms, through a process that closely resembles avoided crossing.