Rotating black hole solutions in relativistic analogue gravity

Modern meta-materials allow one to construct electromagnetic media with almost arbitrary bespoke permittivity, permeability, and magneto-electric tensors. If (and only if) the permittivity, permeability, and magneto-electric tensors satisfy certain stringent compatibility conditions, can the meta-material be fully described (at the wave optics level) in terms of an effective Lorentzian metric -an analogue spacetime. We shall consider some of the standard black-hole spacetimes of primary interest in general relativity, in various coordinate systems, and determine the equivalent meta-material susceptibility tensors in a laboratory setting. In static black hole spacetimes (Schwarzschild and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the horizon. In stationary black hole spacetimes (Kerr and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the ergo-surface.

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“…The "Gordon form" of the Schwarzschild metric [26,27] is less well-known than perhaps is should be. We now consider…”

Section: Cartesian Gordon Formmentioning

confidence: 99%

Bespoke analogue space-times: meta-material mimics

Schuster

Visser

2018

Gen Relativ Gravit

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“…Taken as a whole, these observations collectively give us confidence that it is likely to be possible to mimic the Kerr solution at the wave optics or wave acoustics level -presumably through some "Kerr-Gordon" form of the metric. It is already known that the Schwarzschild metric can be put into Gordon form [41,53]:…”

Section: Discussionmentioning

confidence: 99%

Vorticity in analogue spacetimes

et al. 2019

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Analogue spacetimes can be used to probe and study physically interesting spacetime geometries by constructing, either theoretically or experimentally, some notion of an effective Lorentzian metric [g eff (g, V, Ξ)] ab . These effective metrics generically depend on some physical background metric g ab , often flat Minkowski space η ab , some "medium" with 4-velocity V a , and possibly some additional background fields Ξ. Electromagnetic analogue models date back to the 1920s, acoustic analogue models to the 1980s, and BEC-based analogues to the 1990s. The acoustic analogue models have perhaps the most rigorous mathematical formulation, and these acoustic analogue models really work best in the absence of vorticity, if the medium has an irrotational flow. This makes it difficult to model rotating astrophysical spacetimes, spacetimes with non-zero angular momentum, and in the current article we explore the extent to which one might hope to be able to model astrophysical spacetimes with angular momentum, (thereby implying vorticity in the 4-velocity of the medium). (Stefano Liberati), sebastian.schuster@sms.vuw.ac.nz (Sebastian Schuster ), gtricell@sissa.it (Giovanni Tricella), matt.visser@sms.vuw.ac.nz (Matt Visser ) the exercises in the Landau-Lifshitz volume on classical field theory [6]. Scientific interest in these electromagnetic analogues is ongoing, see for instance [7,8,9,10,11,12,13,14,15], and references therein.In 1981 Unruh developed the acoustic analogue spacetimes (subsequently called dumb holes) [16], with further developments due to one of the present authors [17,18,19]. While these early acoustic models were based on ordinary barotropic fluid mechanics, much subsequent work was based on the "Madelung fluid" interpretation of a quantum condensate wave-function -typically a non-relativistic or relativistic BEC [20,21,22,23,24,25, 26,27,28]. Such analogue models have been applied in mimicking several interesting spacetimes. However, angular momentum in the physical spacetime to be mimicked corresponds to vorticity in the flow of the arXiv:1802.04785v2 [gr-qc]

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“…Because superradiance 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 [8], [9], [10], [11], [12]. Thus far, theoretical and computational investigation of the analogue superradiance have been reported for liquid systems [13], [14], relativistic fluids [15], shallow water systems [16] and optic systems [17], [18], [19], [20]. Within the context of BEC, superradiance stemming from the coherent light matter interaction [21], [22], as an analogue to the Dicke effect [23] and the amplification of matter waves as a manifestation of Raman superradiant scattering were also reported theoretically [24].…”

Section: Introductionmentioning

confidence: 99%

Analog black holes and energy extraction by super-radiance from Bose Einstein condensates (BEC) with constant density

Demirkaya

Dereli

Güven

2019

Heliyon

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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...

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Rotating black hole solutions in relativistic analogue gravity

Cited by 23 publications

References 24 publications

Bespoke analogue space-times: meta-material mimics

Bespoke analogue space-times: meta-material mimics

Vorticity in analogue spacetimes

Analog black holes and energy extraction by super-radiance from Bose Einstein condensates (BEC) with constant density

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