论文标题
半线性波模型，用于临界崩溃
A semi-linear wave model for critical collapse
论文作者
论文摘要
在球形对称性中，引人注目的数值证据表明，在黑洞形成阈值附近的一般相对性溶液中表现出关键行为。其中一个方面是，阈值解决方案本身是自相似的，在某种意义上是独特的。在某种程度上尚未充分理解，相同的现象持续了球形对称性。因此，希望构建在爆炸阈值下表现出这种对称性的模型。从波动方程的变形开始，我们讨论具有离散自相似阈值解决方案的模型。我们在爆炸点的过去光锥中研究阈值溶液。在球形对称性中，存在一种独特的关键解决方案。对于更一般的模型，还提出了球形数值演变，并表现出相似的行为。远离球形对称阈值解决方案获得了更多的自由。可以进行不同的爆炸拓扑，即使在本地，关键解决方案也需要重新解释作为参数化的家族。
In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are self-similar and are, in a certain sense, unique. To an extent yet to be fully understood, the same phenomena persist beyond spherical symmetry. It is therefore desirable to construct models that exhibit such symmetry at the threshold of blow-up. Starting with deformations of the wave equation, we discuss models which have discretely self-similar threshold solutions. We study threshold solutions in the past light cone of the blow-up point. In spherical symmetry there is a sense in which a unique critical solution exists. Spherical numerical evolutions are also presented for more general models, and exhibit similar behavior. Away from spherical symmetry threshold solutions attain more freedom. Different topologies of blow-up are possible, and even locally the critical solution needs reinterpretation as a parameterized family.
