We consider two scalar fields interacting through a χ * χφ * φ term in the presence of a Reissner-Nordstrøm black hole. Initially, only χ particles are present. We find that the produced φ particles are localized in a region around the black hole and have a tendency toward condensation provided that φ particles are much heavier than the χ particles. We also find that such a configuration is phenomenologically viable only if the scalars and the black hole have dark electric charges.
The axisymmetric acoustic perturbations in the velocity potential of a Bose-Einstein condensate in the presence of a single vortex behave like minimally coupled massless scalar fields propagating in a curved (1+1) dimensional Lorentzian space-time, governed by the Klein-Gordon wave equation. Thus far, the amplified scattering of these perturbations from the vortex, as a manifestation of the acoustic superradiance, has been investigated with a constant background density. This paper goes beyond by employing a self-consistent condensate density profile that is obtained by solving the Gross-Pitaevskii equation for an unbound BEC. Consequently, the loci of the event horizon and the ergosphere of the acoustic black hole are modified according to the radially varying speed of sound. The superradiance is investigated both for transient features in the time-domain and for spectral features in the frequency domain. In particular, an effective energy-potential function defined in the spectral formulation correlates with the existence and the frequency dependence of the acoustic superradiance. The numerical results indicate that the constant background density approximation underestimates the maximum superradiance and the frequency at which this maximum occurs. *
This paper presents a numerical study of the acoustic superradiance from the single vortex state of a Bose-Einstein condensate (BEC). The draining bathtub model of an incompressible barotropic fluid is adopted to describe the vortex. The propagation of the velocity potential fluctuations are governed by the massless scalar Klein-Gordon wave equation, which establishes the rotating black-hole analogy. Hence, the amplified scattering of these fluctuations from the vortex comprise the superradiance effect. Particular to this study, a coordinate transformation is applied which enables the identification of the event horizon and the ergosphere termwise in the metric. Thus, the respective spectral solutions can be obtained asymptotically at either boundary. Further, the time-domain calculations of the energy of the propagating perturbations and the independently performed reflection coefficient calculations from the asymptotic solutions of the propagating perturbations are shown to be in very good agreement. While the former solution provides the full dynamical behavior of the superradiance, the latter method gives the frequency spectrum of the superradiance as a function of the rotational frequency of the vortex. Hence, a comprehensive analysis of the superradiance effect can be conducted within this workframe. * Analogies in physics enable us to observe a particular phenomenon with the same characteristic features in different systems pertaining to disparate mechanisms and space-time-energy scales. The present study takes on such an analogy between a black hole and a vortex state of a Bose-Einstein condensate and focuses on the Hawking radiation, the superradiance of light from black holes, in the form of an acoustic superradiance of sound from a vortex. The analogy initiated by Unruh's calculations showed the equivalence between the background solution of velocity perturbations on a perfect barotropic, irrotational Newtonian fluid and the Klein-Gordon field propagating in a 4-dimensional pseudo-Riemannian manifold, in which the speed of sound plays the role of speed of light [1], [2].The superradiance phenomenon is the amplification of the waves scattered from a black-hole in the presence of ergoregion and it is characterized by a reflection coefficient larger than unity [3], [4]. Because this phenomenon occurs in the space-time background of rotating black holes,the analogy could be set for a rotating acoustic black-hole in a liquid [5], [6]. The theoretical and computational investigation of the superradiance in various analogous systems have been reported by a number of studies. Basak and Majumdar introduced a DBT model of a water vortex and studied the conditions under which the density fluctuations of the fluid exhibit amplified scattering from the water vortex [7],[8]. The phenomena is also investigated widely for optical systems [9],[10],[11],[12], relativistic fluids [13], shallow water systems [14] .On the other hand, the experimental studies emerged only within the last few years. Experimental realizations...
We consider two scalar fields interacting through a χ * χφ * φ term in the presence of a Reissner -Nordstrøm black hole. Initially, only χ particles are present. We find that the produced φ particles are localized in a region around the black hole and have a tendency towards condensation provided that φ particles are much heavier than the χ particles. We also find that such a configuration is phenomenologically viable only if the scalars and the black hole have dark electric charges.
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