Relativistic singular isothermal toroids

被引:6
作者
Cai, MJ [1 ]
Shu, FH
机构
[1] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA
[2] Natl Tsing Hua Univ, Dept Phys, Hsinchu 30013, Taiwan
基金
美国国家科学基金会;
关键词
black hole physics; relativity;
D O I
10.1086/345357
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We construct self-similar, axisymmetric, time-independent solutions to Einstein's field equations for an isothermal gas with a at rotation curve in the equatorial plane. The metric scales as ds(2) --> alpha(2) ds(2) under the transformation r --> alphar and t --> alpha(1-n)t, where n is a dimensionless measure of the strength of the gravitational field. The solution space forms a two-parameter family characterized by the ratios of the isothermal sound speed and the equatorial rotation speed to the speed of light. The isodensity surfaces are toroids, empty of matter along the rotation axis. Unlike the Newtonian case, the velocity field is not constant on a cylindrical radius because of frame dragging. As the configuration rotates faster, an ergoregion develops in the form of the exterior of a cone centered about the rotation axis. The sequence of solutions terminates when frame dragging becomes infinite and the ergocone closes onto the axis. The fluid velocity of the last solution has a modest value in the midplane but reaches the speed of light on the axis.
引用
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页码:391 / 401
页数:11
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