旋转黑洞周围的水平穿透跨音速吸积盘
Horizon-Penetrating Transonic Accretion Disks around Rotating Black Holes
摘要：
利用Kerr-Schild坐标，在事件视界不存在坐标奇点的情况下，给出了跨音速吸积盘和旋转黑洞绕流的定态流体动力学方程.本文采用两种因果粘性公式，给出了跨音速吸积流在音速点处的边界条件。对于一类因果粘性公式，我们还在粘性点处增加了边界条件，在粘性点处，吸积径向速度几乎等于粘性扩散速度。基于跨音速吸积盘的形式，在给出跨音速解的计算方法后，计算了几种吸积流模型的光滑通过事件视界的视界穿透跨音速解：理想等温流、理想多方流和粘性多方流、平流主导吸积流（ADAF）和相对论状态方程，绝热吸积盘，标准吸积盘，超临界吸积盘。这些解决方案得到了非旋转和旋转的黑洞。计算得到的吸积流即使事件视界或视界内也以小于光速的有限三倍速度坠入黑洞，且视界处吸积流的角速度一般不同于黑洞旋转引起的标架拖曳的角速度.这些特征与在视界处具有坐标奇异性的Boyer-Lindquist坐标所得到的结果形成对比。
英文摘要：
The stationary hydrodynamic equations for the transonic accretion disks and flows around rotating black holes are presented by using the Kerr-Schild coordinate where there is no coordinate singularity at the event horizon. We use two types of the causal viscosity prescription, and the boundary conditions for the transonic accretion flows are given at the sonic point. For one type of the causal viscosity prescription we also add the boundary conditions at the viscous point where the accreting radial velocity is nearly equal to the viscous diffusion velocity. Based on the formalism for the transonic accretion disks, after we present the calculation method of the transonic solutions, the horizon-penetrating transonic solutions which smoothly pass the event horizon are calculated for several types of the accretion flow models: the ideal isothermal flows, the ideal and the viscous polytropic flows, the advection dominated accretion flows (ADAFs) with the relativistic equation of state, the adiabatic accretion disks, the standard accretion disks, the supercritical accretion disks. These solutions are obtained for both non-rotating and rotating black holes. The calculated accretion flows plunge into black hole with finite three velocity smaller than the speed of light even at the event horizon or inside the horizon, and the angular velocities of the accretion flow at the horizon are generally different from the angular velocity of the frame-dragging due to the black hole's rotation. These features contrast to the results obtained by using the Boyer-Lindquist coordinate with the coordinate singularity at the horizon.
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