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 ${\alpha }_{\text{max}}=\sqrt{\frac{32}{27}}$.

arXiv comment6 pages

References in corpus (36)

• Kerr black holes with scalar hair
• Shadows of Kerr black holes with scalar hair
• Kerr black holes with Proca hair
• Stationary Scalar Clouds Around Rotating Black Holes
• Kerr-Newman scalar clouds
• Stationary resonances of rapidly-rotating Kerr black holes
• Kerr-Newman black holes with stationary charged scalar clouds
• Kerr black holes with self-interacting scalar hair: hairier but not heavier
• On the instability regime of the rotating Kerr spacetime to massive scalar perturbations
• A new spin on black hole hair
• Analytic treatment of the black-hole bomb
• Non-linear Q-clouds around Kerr black holes
• Scalarized Hairy Black Holes
• Iron K$\alpha$ line of Kerr black holes with scalar hair
• Myers-Perry black holes with scalar hair and a mass gap
• The large-mass limit of cloudy black holes
• Extremal Kerr-Newman black holes with extremely short charged scalar hair
• The superradiant instability regime of the spinning Kerr black hole
• Inside black holes with synchronized hair
• Rotating black holes can have short bristles
• Myers-Perry black holes with scalar hair and a mass gap: unequal spins
• An all-optical event horizon in an optical analogue of a Laval nozzle
• How fast can a black hole rotate?
• Spinning boson stars and Kerr black holes with scalar hair: the effect of self-interactions
• Wiggly tails: a gravitational wave signature of massive fields around black holes
• A no-short scalar hair theorem for rotating Kerr black holes
• Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime
• Dynamics of fluctuations in an optical analog of the Laval nozzle
• Acoustic clouds: standing sound waves around a black hole analogue
• Superradiant scattering in fluids of light
• Penrose Superradiance in Nonlinear Optics
• Acoustic black-hole bombs and scalar clouds in a photon-fluid model
• Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
• Massive phonons and gravitational dynamics in a photon-fluid model
• Nonlocality and fluctuations near the optical analog of a sonic horizon
• Analogue gravity by an optical vortex. Resonance enhancement of Hawking radiation

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