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-hole-stationary-scalar-field configurations of the photon-fluid model exist in the narrow dimensionless regime $\alpha \equiv {\Omega }_0/m{\Omega }_{\text{H}}\in (1,{\alpha }_{\text{max}})$ with ${\alpha }_{\text{max}}\simeq 1.08$ [here ${\Omega }_{\text{H}}$ is the angular velocity of the black-hole horizon and $\{{\Omega }_0,m\}$ 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 ${\Omega }_{\text{H}}{r}_{\text{H}}\gg 1$ of rapidly-spinning central supporting acoustic black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum $\{{\Omega }_0({\Omega }_{\text{H}},m;n)\}$ which characterizes the stationary bound-state acoustic scalar clouds of the photon-fluid model. Interestingly, it is proved that the critical (maximal) mass parameter ${\alpha }_{\text{max}}$, 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 ${\alpha }_{\text{max}}=\sqrt{\frac{32}{27}}$.

6 pages

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Cited by in corpus (2)

• Analogue simulations of quantum gravity with fluids
• No-short scalar hair theorem for spinning acoustic black holes in a photon-fluid model