Stationary scalar clouds supported by rapidly-rotating acoustic black holes in a photon-fluid model

Abstract

It has recently been proved that, in the presence of vortex flows, the fluctuation dynamics of a rotating photon-fluid model is governed by the Klein-Gordon equation of an effective massive scalar field in a (2 + 1)-dimensional acoustic black-hole spacetime. Interestingly, it has been demonstrated numerically that the rotating acoustic black hole, like the familiar Kerr black-hole spacetime, may support spatially regular stationary density fluctuations (linearized acoustic scalar 'clouds') in its exterior regions. In particular, it has been shown that the composed rotating-acoustic-black-holestationary-scalar-field configurations of the photon-fluid model exist in the narrow dimensionless regime α ≡ Ω0/mΩH ∈ (1, αmax) with αmax ≃ 1.08 [here ΩH is the angular velocity of the black-hole horizon and {Ω0, m} are respectively the effective proper mass and the azimuthal harmonic index of the acoustic scalar field]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the acoustic scalar clouds of the photon-fluid model in the regime ΩHrH ≫ 1 of rapidly-spinning central supporting acoustic black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum {Ω0(ΩH, m; n)} which characterizes the stationary bound-state acoustic scalar clouds of the photon-fluid model. Interestingly, it is proved that the critical (maximal) mass parameter αmax, which determines the regime of existence of the composed acoustic-black-hole-stationary-bound-state-massive-scalar-field configurations, is given by the exact dimensionless relation αmax = 32 27 .

No-short scalar hair theorem for spinning acoustic black holes in a photon-fluid model

“…As explicitly proved in [27], the effective lengths of the co-rotating non-spherically symmetric scalar cloudy configurations of the spinning Kerr spacetime [19,22] also conform to the lower bound (3). Interestingly, it is well established that fluid systems share many features with curved black-hole spacetimes (see [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] and references therein). In particular, it has recently been proved in the physically important work [28] that acoustic black holes of the (2+1)-dimensional rotating photon-fluid system can support stationary bound-state density fluctuations (acoustic scalar 'clouds') whose spatio-temporal behavior in the black-hole spacetime is governed by the linearized Klein-Gordon equation of an effective massive scalar field.…”

“…As demonstrated numerically in [28] and proved analytically in [43], the stationary bound-state acoustic-black-holemassive-scalar-field cloudy configurations of the photon-fluid model, which respect the boundary conditions ( 10) and (11), are characterized by the dimensionless regime of existence…”