近日，印度金奈数学研究所的的Gopal Yadav及其研究团队取得一项新进展。他们对宇宙奇点、全息复杂度和纠缠进行了研究。相关研究成果已于2024年7月12日在国际知名学术期刊《高能物理杂志》上发表。

该团队研究了具有类Kasner奇点的各种全息宇宙学族的全息体积复杂度，特别聚焦于具有AdS、超尺度违反及Lifshitz渐近性质的全息宇宙学模型。通过大量的数值研究，研究人员发现复杂曲面总是向远离奇点的方向弯曲，并从边界附近的类空间过渡到内部的类光结构。当边界锚定的时间切片逐渐逼近奇点时，这种向类光特性的转变速度显著加快，而类空间部分则相应缩减。

复杂性泛函在类光区域的贡献逐渐消失，因此在奇点附近，复杂性逐渐变小，这表明存在复杂性逐渐降低的双重Kasner状态，也表明在奇点附近对偶的有效自由度极度变薄。

此外，他们还进一步发展了先前对全息纠缠熵的极端表面的研究，并发现在红外极限下它们表现出与复杂性相似的行为。

附：英文原文

Title: Cosmological singularities, holographic complexity and entanglement

Author: Narayan, K., Saini, Hitesh K., Yadav, Gopal

Issue&Volume: 2024-07-12

Abstract: We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with AdS, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.

DOI: 10.1007/JHEP07(2024)125

Source: https://link.springer.com/article/10.1007/JHEP07(2024)125