标题： 高维黑洞临界塌缩：连续自相似解 显示英文标题

标题： Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions

摘要： 我们研究在时空维度数量很大的极限下黑洞临界塌缩的动力学，$D$。 特别是，我们研究了无质量、尺度不变的标量场的球对称引力塌缩，该标量场具有连续自相似性（CSS）。 维度数量很大提供了自然的尺度分离，在每个尺度上不同效应占主导地位，从而简化了运动方程。 通过这种近似方案，我们为此类解构造了匹配渐近解，包括临界解。 然后，我们计算了打破CSS的线性扰动下的黑洞质量临界指数，发现其在无限维度下趋于一个常数值。 此外，我们提出了这些解与具有维度相关状态方程和宇宙学常数的闭合弗里德曼-勒梅特-罗伯逊-沃尔克（FLRW）宇宙学之间的联系。 临界解对应于不稳定的类似爱因斯坦的宇宙，而亚临界和超临界解分别对应于反弹和坍缩的宇宙学。 我们的结果为大-$D$展开作为引力塌缩中的强大解析工具提供了概念验证，并暗示了向其他自相似系统的潜在扩展。 显示英文摘要

摘要： We investigate the dynamics of black hole critical collapse in the limit of a large number of spacetime dimensions, $D$. In particular, we study the spherical gravitational collapse of a massless, scale-invariant scalar field with continuous self-similarity (CSS). The large number of dimensions provides a natural separation of scales, simplifying the equations of motion at each scale where different effects dominate. With this approximation scheme, we construct matched asymptotic solutions for this family, including the critical solution. We then compute the mass critical exponent of the black hole for linear perturbations that break CSS, finding that it asymptotes to a constant value in infinite dimensions. Additionally, we present a link between these solutions and closed Friedmann--Lema\^itre--Robertson--Walker (FLRW) cosmologies with a dimension-dependent equation of state and cosmological constant. The critical solution corresponds to an unstable Einstein-like universe, while subcritical and supercritical solutions correspond to bouncing and crunching cosmologies respectively. Our results provide a proof of concept for the large-$D$ expansion as a powerful analytic tool in gravitational collapse and suggest potential extensions to other self-similar systems.