arXiv subjects

Florent Michel

Publications and source records attributed to Florent Michel.

27 records · Page 2Linked to original sources

arXiv2015

Slow Sound in a duct, effective transonic flows and analogue black holes

We propose a new system suitable for studying analogue gravity effects, consisting of a gas flowing in a duct with a compliant wall. Effective transonic flows are obtained from uniform, low Mach number flows through the reduction of the one-dimensional speed of sound induced by the wall compliance. We show that the modified equation for linear perturbations can be written in a Hamiltonian form. We perform a one-dimensional reduction consistent with the canonical formulation, and deduce the analogue metric along with the first dispersive term. In a weak dispersive regime, the spectrum emitted from a sonic horizon is numerically shown to be Planckian, and with a temperature fixed by the analogue surface gravity.

gr-qc↗

arXiv2015

Mode mixing in sub- and trans-critical flows over an obstacle: When should Hawking's predictions be recovered?

We reexamine the scattering coefficients of shallow water waves blocked by a stationary counter current over an obstacle. By considering series of background flows, we show that the most relevant parameter is $F_{\rm max}$, the maximal value of the ratio of the flow velocity over the speed of low frequency waves. For subcritical flows, i.e., $F_{\rm max} < 1$, there is no analogue Killing horizon and the mode amplification is strongly suppressed. Instead, when $F_{\rm max} \gtrsim 1.1$, the amplification is enhanced at low frequency and the spectrum closely follows Hawking's prediction. We further study subcritical flows close to that used in the Vancouver experiment. Our numerical analysis suggests that their observation of the "thermal nature of the mode conversion" is due to the relatively steep slope on the upstream side and the narrowness of the obstacle.

gr-qc↗

arXiv2015

Black hole radiation in the presence of a universal horizon

In Hořava and Einstein-Æther theories of modified gravity, in spite of the violation of Lorentz invariance, spherically-symmetric stationary black hole solutions possess an inner universal horizon which separates field configurations into two disconnected classes. We compute the late time radiation emitted by a dispersive field propagating in such backgrounds. We fix the initial conditions on stationary modes by considering a regular collapsing geometry, and imposing that the state inside the infalling shell is vacuum. We find that the mode pasting across the shell is adiabatic at late time (large inside frequencies). This implies that large black holes emit a thermal flux with a temperature fixed by the surface gravity of the Killing horizon. In turn, this suggests that the universal horizon should play no role in the thermodynamical properties of these black holes.

gr-qc↗

arXiv2015

Non-linear effects in time-dependent transonic flows: An analysis of analogue black hole stability

We study solutions of the one-dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms, time-dependent flows exhibit a wide variety of behaviors. When the sound speed is crossed once, we observe that flows analogous to black holes obey something similar to the so-called no hair theorem since their late time profile is stationary and uniquely fixed by parameters entering the Hamiltonian and conserved quantities. For flows analogous to white holes, at late time one finds a macroscopic undulation in the supersonic side which has either a fixed amplitude, or a widely varying one signaling a quasi periodic emission of solitons on the subsonic side. When considering flows which cross the sound speed twice, we observe various scenarios which can be understood from the above behaviors, and from the hierarchy of the growth rates of the dynamical instabilities characterizing such flows.

gr-qc↗

arXiv2015

Suppression of infrared instability in trans-sonic flows by condensation of zero-frequency short wave length phonons

We analyze the peculiar infrared instability that characterizes stationary inhomogeneous flows when their velocity crosses the sound speed by decreasing values. For definiteness, we work in the context of one dimensional atomic Bose condensates. These flows are unstable under ultra low real frequency perturbations because of the unbounded mode amplification near the sonic horizon. This results in a condensation of low frequency phonons which produces a spatially structured flow in the supersonic domain. Numerical simulations reveal that this zero-frequency undulation suppresses the instability when its spatial extension is infinite, and when its phase is near that of a "shadow soliton" solution attached to the sonic horizon. These phenomena are akin to the condensation of rotons in flowing superfluid helium-4 when exceeding the Landau velocity. They also pertain to shallow water waves propagating on transcritical flows.

gr-qc↗

arXiv2015

Wave blocking and partial transmission in subcritical flows over an obstacle

We study and measure the transmission coefficient of counter-propagating shallow-water waves produced by a wave generator and scattered by an obstacle. To precisely compare theoretical predictions and experimental data, we consider $\sim 25$ frequencies for 5 subcritical background flows, where the maximum value of the Froude number ranges from $0.5$ to $0.75$. For each flow, the transmission coefficient displays a sharp transition separating total transmission from wave-blocking. Both the width and the central frequency of the transition are in good agreement with their theoretical values. The shape of the obstacle is identical to that used by the Vancouver team in the recent experiment aiming at detecting the analogue of stimulated Hawking radiation. Our results are compatible with the observations that have been reported. They complete them by establishing that the contribution of the transmission coefficient cannot be neglected for the lower half of the probed frequency range.

gr-qc↗

arXiv2014

Probing the thermal character of analogue Hawking radiation for shallow water waves?

We study and numerically compute the scattering coefficients of shallow water waves blocked by a stationary counterflow. When the flow is transcritical, the coefficients closely follow Hawking's prediction according to which black holes should emit a thermal spectrum. We study how the spectrum deviates from thermality when reducing the maximal flow velocity, with a particular attention to subcritical flows since these have been recently used to test Hawking's prediction. For such flows, we show that the emission spectrum is strongly suppressed, and that its Planckian character is completely lost. For low frequencies, we also show that the scattering coefficients are dominated by elastic hydrodynamical channels. Our numerical results reproduce rather well the observations made by S. Weinfurtner {\it et al.} in the Vancouver experiment. Nevertheless, we propose a new interpretation of what has been observed, as well as new experimental tests.

gr-qc↗

arXiv2013

Saturation of black hole lasers in Bose-Einstein condensates

To obtain the end-point evolution of the so-called black hole laser instability, we study the set of stationary solutions of the Gross-Pitaevskii equation for piecewise constant potentials which admit a homogeneous solution with a supersonic flow in the central region between two discontinuities. When the distance between them is larger than a critical value, we recover that the homogeneous solution is unstable, and we identify the lowest energy state. We show that it can be viewed as determining the saturated value of the first (node-less) complex frequency mode which drives the instability. We also classify the set of stationary solutions and establish their relation both with the set of complex frequency modes and with known soliton solutions. Finally, we adopt a procedure à la Pitaevski-Baym-Pethick to construct the effective functional which governs the transition from the homogeneous to non-homogeneous solutions.

cond-mat.quant-gas↗

arXiv2012

Gravitating superconducting strings with timelike or spacelike currents

We construct gravitating superconducting string solutions of the U(1)_{local} x U(1)_{global} model solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on the ratio between the symmetry breaking scale and the Planck mass. Using the macroscopic stability conditions formulated by Carter, we observe that the coupling to gravity allows for a new stable region that is not present in the flat space-time limit. We match the asymptotic metric to the Kasner metric and show that the relations between the Kasner coefficients and the energy per unit length and tension suggested previously are well fulfilled for symmetry breaking scale much smaller than the Planck mass. We also study the solutions to the geodesic equation in this space-time. While geodesics in the exterior space-time of standard cosmic strings are just straight lines, test particles experience a force in a general Kasner space-time and as such bound orbits are possible.

hep-th↗