近日，冰岛大学Mohan, Vyshnav团队研究了全息复杂性中的黑洞奇点。相关论文于2025年7月29日发表在《高能物理杂志》上。

利用复杂性第二定律，研究组证明了黑洞奇点定理。通过引入捕获极值曲面的概念，证明了它们的存在意味着全局双曲型黑洞内零测地线不完备性。研究组还证明了极值表面体积增长率的消失为黑洞奇点提供了一个尖锐的诊断。在静态的、不带电的、球对称的时空中，这对应于类空间极值表面的增长率在奇点处趋于零。在带电或旋转的时空中，比如Reissner-Nordstrm和克尔黑洞，研究组确定了在类时奇点处表现出相同行为的新型类时极端表面。

附：英文原文

Title: Black hole singularities from holographic complexity

Author: Mohan, Vyshnav

Issue&Volume: 2025-07-29

Abstract: Using a second law of complexity, we prove a black hole singularity theorem. By introducing the notion of trapped extremal surfaces, we show that their existence implies null geodesic incompleteness inside globally hyperbolic black holes. We also demonstrate that the vanishing of the growth rate of the volume of extremal surfaces provides a sharp diagnostic of the black hole singularity. In static, uncharged, spherically symmetric spacetimes, this corresponds to the growth rate of spacelike extremal surfaces going to zero at the singularity. In charged or rotating spacetimes, such as the Reissner-Nordstrm and Kerr black holes, we identify novel timelike extremal surfaces that exhibit the same behavior at the timelike singularity.

DOI: 10.1007/JHEP07(2025)275

Source: https://link.springer.com/article/10.1007/JHEP07(2025)275