标题： 广义相对论的双曲形式中黑洞的数值演化 显示英文标题

标题： Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity

摘要： 我们描述了一个数值代码，用于求解球对称的施瓦茨希尔德黑洞的爱因斯坦方程，使用了由Choquet-Bruhat和York引入的双曲形式。这是首次使用这种形式来演化包含黑洞的数值时空。为了避开中心奇点，我们将黑洞从计算网格中切除。我们详细描述了一种因果差分方法，该方法应允许在三个空间维度中使用任意位移向量稳定地演化双曲方程组，空间和时间上均为二阶精度。我们在球对称情况下展示了该方法的成功。 显示英文摘要

摘要： We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.