Excised acoustic black holes: The scattering problem in the time domain

Abstract

The scattering process of a dynamic perturbation impinging on a draining-tub model of an acoustic black hole is numerically solved in the time domain. Analogies with real black holes of General Relativity are explored by using recently developed mathematical tools involving finite elements methods, excision techniques, and constrained evolution schemes for strongly hyperbolic systems. In particular it is shown that superradiant scattering of a quasi-monochromatic wavepacket can produce strong amplification of the signal, offering the possibility of a significant extraction of rotational energy at suitable values of the angular frequency of the vortex and of the central frequency of the wavepacket. The results show that theoretical tools recently developed for gravitational waves can be brought to fruition in the study of other problems in which strong anisotropies are present.

Analogue Gravity

“…Quasinormal modes have again received attention in [78], while the Magnus force is reanalysed in terms of the acoustic geometry in [432]. Singularities in the acoustic geometry are considered in [56], while back-reaction has received more attention in [343].…”

From Quantum Hydrodynamics to Quantum Gravity

“…In particular, it was suggested to use the renormalization techniques developed in QFT to study the depletion of BEC; 4 in other presentation the stability of sonic horizons in BEC 5 and the scattering problems on rotating acoustic black holes have been discussed. 6 Effective metric appears for light propagating in non-linear dispersive dielectric media 7 and in moving media; 8 for surface waves -ripplons -propagating on the surface of quantum liquids or at the interface between two superfluids. 9 The latter allows us to study experimentally the instability of the quantum vacuum in ergoregion.…”

Acoustic superradiance from an optical-superradiance-induced vortex in a Bose-Einstein condensate

“…The method has been implied in Refs. [7,28] and the superradiance state has been discussed in detail. In the case of our system the problem becomes even more difficult since the equation must be solved along with the linearized equations of motions for δα 1 , δα 2 , and δα 3 .…”