Fluid analogs for rotating black holes

Abstract

Fluid analog models for gravity are based on the idea that any spacetime geometry admits a reinterpretation in which space is thought of as a fluid flowing with a prescribed velocity. This fluid picture is a restatement of the ADM decomposition of the metric. Most of the literature has focused on flat spatial geometries and physical fluid flows, with a view toward possible laboratory realizations. Here we relax these conditions and consider fluid flows on curved and time-dependent spatial geometries, as a way of understanding and visualizing solutions to general relativity. We illustrate the utility of the approach with rotating black holes. For the Kerr black hole we develop a fluid description based on Doran coordinates. For spinning BTZ black holes we develop two different fluid descriptions. One involves static conical spatial slices, with the fluid orbiting the tip of the cone. The other resembles a cosmology, with the fluid flowing on a time-dependent cylindrical geometry.

Radiation shielding of analog Bañados-Teitelboim-Zanelli black holes

“…其中 0  是流体密度，   0 c  是局部声速， () vx 是流体速度。 类比黑洞第一次将天体物理的霍金辐射效应 [2] 和实验室模拟系统联系起 来。随后在玻色爱因斯坦凝聚体 [3] ，极化流体 [4] 和水流 [5] 中都给出了(1+1)维 的黑洞视界。 (1+1)维类比黑洞可以看作 Painleve Gullstrand Lemaitre   坐标 下 [6][7][8] 的(1+1)维的史瓦西黑洞的类比 [9,10]…”

Regular frames and particle’s rotation near a black hole

“…The divergences of n are connected with the fact that the original coordinates (like the Boyer-Lindquist ones for the Kerr metric) fail near the horizon, so both t and the polar angle variable φ diverge. Meanwhile, in recent years, coordinate frames regular near the rotating black holes were constructed [2]- [5] that enabled one to trace rather subtle details of particle behavior near the horizon [6], [7] or give physical interpretation of metrics in terms of rotating fluid [8]. The aim of the present work is to consider the properties of revolution of a particle around a black hole using this type of angle variable.…”