发表机构
Asia Pacific Center for Theoretical Physics; Pohang University of Science and Technology（亚太理论物理中心; 浦项科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过数值模拟发现原初曲率扰动并非一对一形成原初黑洞，引入新诊断量并补充线性表面强度，表明坍缩结果还与曲率环境的空间范围等因素相关。
AI 中文摘要
原初黑洞（PBH）的计算通常将罕见的曲率峰视为孤立的坍缩区域。我们利用辐射主导宇宙中的完全非线性3+1数值相对论模拟表明，相邻的原初曲率扰动并非必须一对一映射到PBH：它们可能最终弥散、集体坍缩为单个PBH，或发生不同的局域坍缩并形成多个PBH。在本研究的双组分轮廓族中，后一种结果是一对PBH，其特征是在至少一个时间片上存在两个不相连的表观视界。我们引入了一种基于霍金质量的非球对称准局域致密性诊断量，该诊断量参考了面积相等的平直FLRW球。它保留了曲率场的角结构，并在球对称情况下简化为标准的Misner-Sharp致密性函数。该诊断量的全局最大值$\boldsymbol{\textit{K}}_{\rm form}$提供了至少形成一个PBH的经验指标，其转变点约为$\boldsymbol{\textit{K}}_{\rm form,c}\boldsymbol{\textit{\textbf{≈0.56}}}$，且存在适度的、依赖于轮廓的离散性。对于形成双峰轮廓的情况，我们在相同探测球上评估的带符号线性表面强度补充了非线性致密性信息。较弱局域分支的可行性以及局域与共同包围分支之间的竞争，提高了单PBH与双PBH结果之间的经验区分度。因此，我们的结果表明，仅最大曲率振幅无法决定坍缩结果，还取决于周围曲率环境的空间范围、特征尺度和几何结构。
英文摘要
Primordial black hole (PBH) calculations usually treat rare curvature peaks as isolated collapsing regions. Using fully nonlinear $3+1$ numerical-relativity simulations in a radiation-dominated Universe, we demonstrate that neighbouring primordial curvature perturbations need not map one-to-one onto PBHs: they may ultimately disperse, collapse collectively into a single PBH, or undergo distinct local collapses and form more than one PBH. In the family of two-component profiles studied here, the latter outcome is a pair of PBHs, identified by the coexistence of two disconnected apparent horizons on at least one time slice. We introduce a nonspherical quasi-local compaction diagnostic based on the Hawking mass and referenced to a round flat-FLRW sphere of equal area. It retains the angular structure of the curvature field and reduces to the standard Misner-Sharp compaction function in spherical symmetry. The global maximum of this diagnostic, $\mathcal K_{\rm form}$, provides an empirical indicator of whether at least one PBH forms, with a transition near $\mathcal K_{\rm form,c}\approx0.56$ and modest profile-dependent scatter. For forming bimodal profiles, we supplement the nonlinear compactness with a signed linear surface strength evaluated on the same probing spheres. The viability of the weaker local branch and the competition between the local and common-enclosing branches improve the empirical discrimination between single- and double-PBH outcomes. Our results therefore show that the maximum curvature amplitude alone does not determine the collapse outcome, which also depends on the spatial extent, characteristic scales, and geometry of the surrounding curvature environment.
Comments23 pages, 10 figures
