Superresonance  from a rotating acoustic black hole

Abstract

Using the analogy between a shrinking fluid vortex ('draining bathtub'), modelled as a (2+1) dimensional fluid flow with a sink at the origin, and a rotating (2+1) dimensional black hole with an ergosphere, it is shown that a scalar sound wave is reflected from such a vortex with an amplification for a specific range of frequencies of the incident wave, depending on the angular velocity of rotation of the vortex. We discuss the possibility of observation of this phenomenon, especially for inviscid fluids like liquid HeII, where vortices with quantized angular momentum may occur.The possibility of experimental observation of the acoustic analog of Hawking radiation from regions of flow of inviscid and barotropic fluids behaving as outer trapped surfaces ('acoustic event horizons'), was pointed out by Unruh [1] more than two decades ago. Recent advances in theoretical understanding of such acoustic analogs of black holes, as well as improved experimental techniques involving Bose-Einstein condensates [2] have brought such experimental possibilities within the realm of reality. A variety of fluid flow configurations have been identified, all of which can now be described in terms of different analog black hole models [3]. Many of these can actually be realized in the laboratory under cryogenic conditions; thus, the analogy enables laboratory tests of a class of phenomena associated with those aspects of black hole physics that are insensitive to whether or not the metric satisfies the Einstein equation.While attention so far has been focussed on the observation of Hawking radiation from these acoustic black holes, the question of possible energy extraction from these analogs via the Penrose process [4] also needs to be addressed. This process requires black holes with angular momentum. The analogous situation would correspond to fluid flow with rotation, possessing a region of supersonic flow analogous to the ergosphere of a Kerr black hole, surrounding the horizon. In the case of the Kerr black hole, a scalar wave (a solution of the massless Klein-Gordon equation in the black hole spacetime), entering the ergosphere, is reflected back outside with an amplitude that exceeds the amplitude of the incident wave, for a certain range of frequencies bounded from above by the angular velocity of the black hole. The wave extracts energy from the rotational energy of the hole, leading to a 'spin-down' of the latter. This wave-analog of the Penrose process was discovered by Zeldovich [5] and investigated in detail by Starobinsky [6] and Misner (who dubbed the phenomenon 'superradiance') [7].In this paper, we investigate the possibility of the acoustic analog of superradiance (a phenomenon that we call 'superresonance'), i.e., the amplification of a sound wave by reflection from the 'ergo'-region of a rotating acoustic black hole. For the latter, we choose the so-called 'draining bathtub' type of fluid flow [3], which is basically a 2+1 dimensional flow with a sink at the origin. A two surface in this flow, on which the flu...

Acoustic clouds: Standing sound waves around a black hole analogue

“…Superradiant scattering of acoustic waves can be seen in this type of geometries, without the need of introducing a cavity [4,8,34]. To obtain acoustic clouds, however, we need to consider ω ¼ ω c and introduce a mirror at r ¼ r 0 where boundary conditions of Dirichlet [ψ m ðr 0 Þ ¼ 0] or Neumann [dðψ m ðrÞÞ=dr] types are imposed.…”

Quantum Brownian motion in an analog Friedmann-Robertson-Walker geometry

“…The basic idea resides in the fact that the linearized perturbation for an inviscid and irrotational fluid describes the same equation of motion of a massless scalar field in curved spacetime. These mentioned phenomena can be observed in principle if we have to our disposal a system such as a Bose-Einstein condensate (BEC) which has been extensively investigated and seems to constitute an excellent scenario to furnish a possible comprehension of the astrophysical Hawking radiation, particle production in a cosmological scale and superradiance [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Vortices in Bose-Einstein Condensates: Theory

“…For Hawking radiation it is preferable to avoid the generation of vortices [121,128], and as such will not be discussed here. However, the phenomena of superradiance in BECs, which can be considered as stimulated Hawking radiation, relies on the presence of a vortex [129,130,131,132], which is analogous to a rotating black hole.…”

“…This has been studied using Eqs. (12) and (13) for monochromatic sound waves of frequency ω s and angular wave number q s incident upon a vortex [129] and a 'draining vortex" (a vortex with outcoupling at its center) [130,131,132].…”

“…Assuming a homogeneous density n and a velocity profile v(r, θ) = −car + Ωa 2θ /r where c is the homogeneous speed of sound, superradiance occurs when 0 < ω s < q s Ω [130,131,132]. The increase in energy of the outgoing sound is due to an extraction of energy from the vortex and as such it is expected to lead to slowing of the vortex rotation.…”