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Description
In the context of Hawking-like radiation in sonic black holes formed by BECs we investigate the modifications of the emission spectrum caused by a finite width of the sonic transition region connecting the subsonic to supersonic flow [1].
Acoustic black holes formed by Bose-Einstein condensates (BEC) undergoing transonic motion have shown the presence of Hawking-like radiation [2,3,4]. The detection is however indirect, since what has been measured are the correlations between the Hawking particles and their negative energy partners [4,5]. The transition from subsonic to supersonic flow usually occurs in an infinitely thin surface, the sonic horizon of the acoustic BH metric according to the gravitational analogy. In this work we study a particular case in which this transition occurs in a region of finite extension, where the flow velocity equals the speed of sound.
We study a simple toy model where the condensate is step-wise homogeneous, i.e. the sound speed profile is a step-wise function and the density of atoms in the condensate remains constant in all regions. Particularly, the model has two semi-infinite regions, one subsonic one supersonic, representing the inside and outside of a black hole, separated by a sonic region of finite length, representing a thick horizon [6].
We show that the real solutions to the dispersion relation in the sonic region are two, as in the subsonic region. This implies that it is the boundary between the supersonic and the sonic regions that produces the spontaneous emission of photons.
We find that:
- Hawking-like emission decreases as the length $a$ of the sonic region increases (as $a^{-2}$ for large $a$); the thick horizon produces a “gray body factor” (Figure 1).
- For sufficiently large values of the sonic region width ‘a’ we see a transition from a (small frequency) $\omega^{-1}$ thermal behaviour to a non-thermal $\omega^{-1/3}$ one. This behaviour is in agreement with the results in a model with two semi-infinite regions, one supersonic and the other sonic.
- For sufficiently large values of $a$ we also find oscillations in the number of Hawking phonons emitted, i.e. suggesting that the sonic region acts as some sort of cavity.
References:
[1] D. Peñalver, M. De Vito, R. Balbinot, and A. Fabbri, Acoustic black holes in BECs with an extended sonic region, Phys. Rev. D 112, L021701 (2025).
[2] W. G. Unruh, Experimental Black-Hole Evaporation?, Phys. Rev. Lett. 46, 1351 (1981).
[3] S. W. Hawking, Particle creation by black holes, Commun.Math. Phys. 43, 199 (1975).
[4] L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Sonic Analog of Gravitational Black Holes in Bose-Einstein Condensates, Phys. Rev. Lett. 85, 4643 (2000).
[5] J. R. Muñoz De Nova, K. Golubkov, V. I. Kolobov, and J. Steinhauer, Observation of thermal Hawking radiation and its temperature in an analogue black hole, Nature 569, 688 (2019).
[6] I. Carusotto, S. Fagnocchi, A. Recati, R. Balbinot, and A. Fabbri, Numerical observation of Hawking radiation from acoustic black holes in atomic Bose–Einstein condensates, New J. Phys. 10, 103001 (2008).