Critical gravitational collapse of a perfect fluid: nonspherical perturbations
Critical gravitational collapse of a perfect fluid: nonspherical perturbations
复制标题
完美流体的临界引力塌缩：非球面扰动
DOI：
10.1103/physrevd.65.084021
复制
发表时间：
1999
影响因子：
5
通讯作者：
Carsten Gundlach
中科院分区：
文献类型：
--
作者：
Carsten Gundlach;Carsten Gundlach
用数值方法构造了球对称理想流体引力崩塌的连续自相似解，并研究了它们的线性摄动，包括球面和非球面的线性扰动.$L=1$轴向摄动允许进行解析处理。所有其他的都是用数字来研究的。对于中间状态方程，对于$1/9l\ensuremath{\kappa}\ensuremath{\lesssim}0.49，$，css解有一个球形增长模式，但没有非球形增长模式。这表明，即使在(轻微)非球形坍塌的情况下，这也是一个关键的解决方案。在这个范围内，我们预测黑洞角动量的临界指数是$5(1+3\ensuremath{\kappa})/3(1+\ensuremath{\kappa})$乘以黑洞质量的临界指数。对于$\EnsureMath{\kappa}=1/3$，这给出了角动量临界指数$\EnsureMath{\Mu}\EnsureMath{\simeq}0.898，$更正了先前的结果。对于刚性状态方程，$0.49\ensuremath{\lesssim}\ensuremath{\kappa}l1，$css解有一个球型和几个非球型增长模式。对于软状态方程，$01\Ensureath{\kappa>L1/9，$CS解有$1+3$增长模式：球形模式和$L=1$轴向模式(其中$m=\Ensureath{-}1，0，1)。$
Continuously self-similar (CSS) solutions for the gravitational collapse of a spherically symmetric perfect fluid, with the equation of state $p=\ensuremath{\kappa}\ensuremath{\rho},$ with $0l\ensuremath{\kappa}l1$ a constant, are constructed numerically and their linear perturbations, both spherical and nonspherical, are investigated. The $l=1$ axial perturbations admit an analytical treatment. All others are studied numerically. For intermediate equations of state, with $1/9l\ensuremath{\kappa}\ensuremath{\lesssim}0.49,$ the CSS solution has one spherical growing mode, but no nonspherical growing modes. That suggests that it is a critical solution even in (slightly) nonspherical collapse. For this range of $\ensuremath{\kappa}$ we predict the critical exponent for the black hole angular momentum to be $5(1+3\ensuremath{\kappa})/3(1+\ensuremath{\kappa})$ times the critical exponent for the black hole mass. For $\ensuremath{\kappa}=1/3$ this gives an angular momentum critical exponent of $\ensuremath{\mu}\ensuremath{\simeq}0.898,$ correcting a previous result. For stiff equations of state, $0.49\ensuremath{\lesssim}\ensuremath{\kappa}l1,$ the CSS solution has one spherical and several nonspherical growing modes. For soft equations of state, $0l\ensuremath{\kappa}l1/9,$ the CSS solution has $1+3$ growing modes: a spherical one, and an $l=1$ axial mode (with $m=\ensuremath{-}1,0,1).$