光子-流体模型中快速旋转声黑洞支持的静止标量云
Stationary scalar clouds supported by rapidly-rotating acoustic black holes in a photon-fluid model
摘要：
最近的研究证明，在有涡流存在的情况下，旋转光子流体模型的涨落动力学是由$(2+1)$维声学黑洞时空中有效质量标量场的Klein-Gordon方程控制的.有趣的是，它已经证明了数字旋转的声学黑洞，像熟悉的克尔黑洞时空，可能支持空间规则的静态密度波动（线性化的声学标量“云”）在其外部区域。特别地，证明了光子流体模型的复合黑洞稳态标量场组态存在于窄无量纲区域$α\equivΩ_0/mΩ_{\text{H}}\in(1,α_{\text{max}})$和$α_{\text{max}}\simeq 1.08$ [这里$Ω_{\text{H}}$是黑洞视界的角速度，$\{Ω_0,m\}$分别是标量场的有效固有质量和方位谐波指数].在本文中，我们使用的分析技术，以探讨的物理和数学性质的声学标量云的光子流体模型的制度$Ω_{\text{H}}r_{\text{H}}\gg1$的快速旋转的中央支持声学黑洞。特别是，我们推导出一个非常紧凑的离散共振谱$\{Ω_0(Ω_{\text{H}},m;n)\}$的解析公式，它表征了静态的光子流体模型的束缚态声学标量云。有趣的是，它被证明的临界（最大）质量参数$α_{\text{max}}$，它决定了该地区的存在的组合声学黑洞稳态束缚态标量场配置，是由精确的无量纲关系$α_{\text{max}}=\sqrt{{{32}\over{27}}}$。
英文摘要：
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 $α\equivΩ_0/mΩ_{\text{H}}\in(1,α_{\text{max}})$ with $α_{\text{max}}\simeq 1.08$ [here $Ω_{\text{H}}$ is the angular velocity of the black-hole horizon and $\{Ω_0,m\}$ 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 $Ω_{\text{H}}r_{\text{H}}\gg1$ of rapidly-spinning central supporting acoustic black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum $\{Ω_0(Ω_{\text{H}},m;n)\}$ which characterizes the stationary bound-state acoustic scalar clouds of the photon-fluid model. Interestingly, it is proved that the critical (maximal) mass parameter $α_{\text{max}}$, 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 $α_{\text{max}}=\sqrt{{{32}\over{27}}}$.
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