4+1维时空中球对称带电标量场的临界和极端引力坍缩

中文摘要 AI 辅助

我们在4+1维时空中，数值研究了与爱因斯坦方程和麦克斯韦方程耦合的带电标量场在球对称性下的引力坍缩。在坍缩阈值处，我们发现了与3+1维中非常相似的第二类临界现象，包括临界解的自相似性以及黑洞质量和电荷的幂律标度。在坍缩区域内部，我们还确定了坍缩成极端黑洞的初始数据。通过将初始数据的所有参数变化高达约0.5%，我们提供了证据表明，在初始数据空间中存在一个小邻域，其中在余维数为1的初始数据集演化中会形成一个精确的极端带电黑洞。我们认为这是从规则初始数据出发的标量场坍缩中首次获得此类证据。

英文摘要

We numerically investigate the gravitational collapse of a charged scalar field coupled to the Einstein and Maxwell equations in spherical symmetry, in 4+1 spacetime dimensions. At the threshold of collapse we find type-II critical phenomena very similar to what is seen in 3+1 dimensions, including self-similarity of the critical solution and power-law scaling of the black hole mass and charge. Well inside the collapse region, we also identify initial data that collapse to an extremal black hole. By varying all parameters of the initial data by up to $\sim0.5\%$, we give evidence that there is a small neighbourhood in the space of initial data where an exactly extremal charged black hole is formed in the evolution of a codimension-1 set of initial data. We believe this is the first such evidence for scalar field collapse from regular initial data.

发表机构

• Ludwig-Maximilians-Universität München（慕尼黑大学）
• University of Southampton（南安普顿大学）

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