DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Rev Lett. 2013 Apr 26;110(17):171602. doi: 10.1103/PhysRevLett.110.171602.
We explore use of the harmonic Einstein equations to numerically find stationary black holes where the problem is posed on an ingoing slice that extends into the interior of the black hole. Requiring no boundary conditions at the horizon beyond smoothness of the metric, this method may be applied for horizons that are not Killing. As a nontrivial illustration we find black holes which, via AdS-CFT, describe a time-independent CFT plasma flowing through a static spacetime which asymptotes to Minkowski in the flow's past and future, with a varying spatial geometry in between. These are the first nonperturbative examples of stationary black holes which do not have Killing horizons. When the CFT spacetime slowly varies, the CFT stress tensor derived from gravity is well described by viscous hydrodynamics. For fast variation it is not, and the solutions are stationary analogs of dynamical quenches, with the plasma being suddenly driven out of equilibrium. We find evidence these flows become unstable for sufficiently strong quenches, and speculate the instability may be turbulent.
我们探索使用调和爱因斯坦方程在一个渐入式切片上数值求解静态黑洞，该切片延伸到黑洞内部。由于不需要在视界处施加任何边界条件，除了要求度规的光滑性之外，这种方法可以应用于非 Kiling 视界。作为一个非平凡的例子，我们发现了黑洞，通过 AdS-CFT，描述了一个时间独立的 CFT 等离子体通过静态时空流动，该时空在流动的过去和未来渐近于闵可夫斯基时空，而在两者之间存在变化的空间几何形状。这些是第一个没有 Kiling 视界的静态黑洞的非微扰实例。当 CFT 时空缓慢变化时，从引力中导出的 CFT 应力张量可以很好地用粘性流体力学来描述。对于快速变化，它不适用，并且这些解是动力学淬火的静态类比，等离子体突然被驱出平衡。我们发现证据表明，对于足够强的淬火，这些流变得不稳定，并推测这种不稳定性可能是湍流的。
