Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves
Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves
复制标题
轴对称的约束演化和长长布里尔波的引力塌缩
DOI：
10.1088/0264-9381/25/13/135009
复制
发表时间：
2008
影响因子：
3.5
通讯作者：
O. Rinne
中科院分区：
文献类型：
--
作者：
O. Rinne
本文研究轴对称真空时空中的爱因斯坦方程。我们考虑了在每个时间步解约束方程和椭圆规范条件的数值演化格式。我们研究了文献中提出的两种这样的方案，并表明它们的一些椭圆方程是不定的，因此可能承认非唯一解，并导致基于经典松弛方法的数值解失效。然后提出了一种不受这些问题影响的新方案。我们用我们的数值实现来研究布里尔波的引力坍缩。一个高度延伸的波会形成黑洞而不是裸奇点。
This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such schemes that have been proposed in the literature and show that some of their elliptic equations are indefinite, thus potentially admitting nonunique solutions and causing numerical solvers based on classical relaxation methods to fail. A new scheme is then presented that does not suffer from these problems. We use our numerical implementation to study the gravitational collapse of Brill waves. A highly prolate wave is shown to form a black hole rather than a naked singularity.