求解哈密顿约束的另一种方法
An alternative approach to solving the Hamiltonian constraint
摘要：
求解爱因斯坦约束方程构造黑洞初始数据需要处理黑洞奇点。通常情况下，这是这样做的切除方法，其中的黑洞内部被切除的数值网格，或穿刺的方法，其中的奇异部分的共形因子表示在一个分析的背景解决方案，然后解决的哈密顿约束的背景解决方案，通常，被假定为定期无处不在的校正。我们讨论了另一种方法，在该方法中的哈密顿约束求解的共形因子的逆功率。这个新函数在任何地方都是有限的，因此这种方法既不需要切除，也不需要分裂成背景和校正。特别地，即使当对共形因子的校正本身是奇异的时，该方法也可以在不修改的情况下使用。我们证明了这一功能的旋转黑洞的喇叭拓扑结构。
英文摘要：
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from the numerical grid, or with the puncture method, in which the singular part of the conformal factor is expressed in terms of an analytical background solution, and the Hamiltonian constraint is then solved for a correction to the background solution that, usually, is assumed to be regular everywhere. We discuss an alternative approach in which the Hamiltonian constraint is solved for an inverse power of the conformal factor. This new function remains finite everywhere, so that this approach requires neither excision nor a split into background and correction. In particular, this method can be used without modification even when the correction to the conformal factor is singular itself. We demonstrate this feature for rotating black holes in the trumpet topology.
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