The critical collapse of a scalar field is a threshold solution of black hole formation, in which a naked singularity arises. We study here the curvature strength of this singularity using a numerical ansatz. The behavior of the Jacobi volume forms is examined along a non-spacelike geodesic in the limit of approach to the singularity. These are seen to be vanishing, thus showing that all physical objects will be crushed to zero size near the singularity. Consequently, although the critical collapse is considered to be a fine-tuning problem, the naked singularity forming is gravitationally strong. This implies that the spacetime cannot be extended beyond the singularity, thus making the singularity genuine and physically interesting. These results imply that the nature of critical collapse may need to be examined and explored further.

标量场的严重崩溃是黑洞形成的阈值解决方案，其中出现了裸奇点。我们在这里使用数值ansatz研究这种奇点的曲率强度。在接近奇点的范围内，沿着非空间测地线检查了Jacobi体形式的行为。这些都消失了，因此表明所有物理对象都将被压缩为接近奇点的零大小。因此，尽管临界塌陷被认为是一个微调问题，但裸奇点形成在重力上很强。这意味着时空不能扩展到超出奇异性，从而使奇异性真实且在物理上很有趣。这些结果表明，关键崩溃的性质可能需要进一步检查和探索。