标题： 非旋转黑洞内部和外部的理想流体动力学：Painlev{é}-Gullstrand坐标下的哈密顿描述 显示英文标题

标题： Ideal hydrodynamics inside as well as outside non-rotating black hole: Hamiltonian description in the Painlev{é}-Gullstrand coordinates

摘要： 结果表明，使用Painlevé-Gullstrand坐标及其准笛卡尔变体时，在非旋转黑洞附近的相对论完美流体力学的哈密顿量泛函仅比相应的平直时空哈密顿量多一项。 此外，由于在Painlevé-Gullstrand坐标中事件视界处没有奇异性，因此可以统一描述黑洞的内部区域和外部区域。 给出了一个精确解，描述了超硬物质（$\varepsilon\propto n^2$）向移动黑洞的定常吸积，直至到达中心奇点。 在局部诱导近似下，导出了在这种吸积背景下薄涡旋管的动力学方程。 显式地计算了具有超相对论状态方程（$\varepsilon\propto n^{4/3}$）的流体的哈密顿量，并解析地解决了这种物质的中心对称定态流动问题。 显示英文摘要

摘要： It is demonstrated that with using Painlev{\'e}-Gullstrand coordinates in their quasi-Cartesian variant, the Hamiltonian functional for relativistic perfect fluid hydrodynamics near a non-rotating black hole differs from the corresponding flat-spacetime Hamiltonian just by a simple term. Moreover, the internal region of the black hole is then described uniformly together with the external region, because in Painlev{\'e}-Gullstrand coordinates there is no singularity at the event horizon. An exact solution is presented which describes stationary accretion of an ultra-hard matter ($\varepsilon\propto n^2$) onto a moving black hole until reaching the central singularity. Equation of motion for a thin vortex filament on such accretion background is derived in the local induction approximation. The Hamiltonian for a fluid having ultra-relativistic equation of state $\varepsilon\propto n^{4/3}$ is calculated in explicit form, and the problem of centrally-symmetric stationary flow of such matter is solved analytically.