Marginally stable resonant modes of the polytropic hydrodynamic vortex

Abstract

The polytropic hydrodynamic vortex describes an effective $(2+1)$-dimensional acoustic spacetime with an inner reflecting boundary at $r=r_{\text{c}}$. This physical system, like the spinning Kerr black hole, possesses an ergoregion of radius $r_{\text{e}}$ and an inner non-pointlike curvature singularity of radius $r_{\text{s}}$. Interestingly, the fundamental ratio $r_{\text{e}}/r_{\text{s}}$ which characterizes the effective geometry is determined solely by the dimensionless polytropic index $N_{\text{p}}$ of the circulating fluid. It has recently been proved that, in the $N_{\text{p}}=0$ case, the effective acoustic spacetime is characterized by an {\it infinite} countable set of reflecting surface radii, $\{r_{\text{c}}(N_{\text{p}};n){\}}_{n=1}^{n=\infty }$, that can support static (marginally-stable) sound modes. In the present paper we use {\it analytical} techniques in order to explore the physical properties of the polytropic hydrodynamic vortex in the $N_{\text{p}}>0$ regime. In particular, we prove that in this physical regime, the effective acoustic spacetime is characterized by a {\it finite} discrete set of reflecting surface radii, $\{r_{\text{c}}(N_{\text{p}},m;n){\}}_{n=1}^{n=N_{\text{max}}}$, that can support the marginally-stable static sound modes (here $m$ is the azimuthal harmonic index of the acoustic perturbation field). Interestingly, it is proved analytically that the dimensionless outermost supporting radius $r_{\text{c}}^{\text{max}}/r_{\text{e}}$, which marks the onset of superradiant instabilities in the polytropic hydrodynamic vortex, increases monotonically with increasing values of the integer harmonic index $m$ and decreasing values of the dimensionless polytropic index $N_{\text{p}}$.

arXiv comment13 pages

References in corpus (24)

• Instability of the massive Klein-Gordon field on the Kerr spacetime
• The black hole bomb and superradiant instabilities
• Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass
• Superradiant instabilities in astrophysical systems
• Stationary Scalar Clouds Around Rotating Black Holes
• Small Kerr-anti-de Sitter black holes are unstable
• Instability of Massive Scalar Fields in Kerr-Newman Spacetime
• Superradiant instabilities of rotating black holes in the time domain
• Rapid growth of superradiant instabilities for charged black holes in a cavity
• Stationary resonances of rapidly-rotating Kerr black holes
• On the instability regime of the rotating Kerr spacetime to massive scalar perturbations
• Time evolution of superradiant instabilities for charged black holes in a cavity
• Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime
• New instability for rotating black branes and strings
• Superradiance from BEC vortices: a numerical study
• Black hole bombs and explosions: from astrophysics to particle physics
• Superradiant scattering from a hydrodynamic vortex
• Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime
• Ergoregion instability: The hydrodynamic vortex
• On the stability of the massive scalar field in Kerr space-time
• Quasinormal modes and Regge poles of the canonical acoustic hole
• Algebraically special resonances of the Kerr-black-hole-mirror bomb
• Onset of superradiant instabilities in the hydrodynamic vortex model
• Quasinormal modes of the polytropic hydrodynamic vortex

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