近日，加拿大麦吉尔大学的Keivan Namjou及其研究团队取得一项新进展。经过不懈努力，他们进行全息宇宙学的新观测。相关研究成果已于2024年10月24日在国际知名学术期刊《高能物理杂志》上发表。
该研究团队考虑考虑双锥几何结构的推广，其中包括位于事件视界和黑洞奇点之间的洛伦兹宇宙学。研究人员在二维和三维空间中对此进行了分析，其中宇宙学具有紧致的空间部分以及大爆炸/大挤压奇点。这些奇点通过使度量略微复杂化而以相同的方式得到规范。
研究人员证明了在满足Kontsevich-Segal准则的同时，这是可能的，这意味着这些几何结构可以解释为广义相对论中微扰稳定的鞍点。这一过程导致了一种用对偶边界共形场论（CFT）中的标准可观测量来描述宇宙学的新方法。
在三维空间中，宇宙学解为边界CFT态密度的两点函数提供了新的贡献。与通常的双锥不同，它描述了不同质量黑洞微态之间的相关性，并且在某个极限下描述了重态统计量与接近BTZ阈值态统计量之间的相关性。
据悉，双锥几何结构是引力路径积分的鞍点，它解释了黑洞微态能谱的混沌统计特性。这种几何结构是通常的反德西特-施瓦茨希尔德（AdS-Schwarzschild）黑洞，但时间坐标具有周期性特征。由此在黑洞视界处产生的奇点，通过使几何结构略微复杂化而得到规范。
附：英文原文
Title: A new observable for holographic cosmology
Author: Chakravarty, Joydeep, Maloney, Alexander, Namjou, Keivan, Ross, Simon F.
Issue&Volume: 2024-10-24
Abstract: The double-cone geometry is a saddle of the gravitational path integral, which explains the chaotic statistics of the spectrum of black hole microstates. This geometry is the usual AdS-Schwarzschild black hole, but with a periodic identification of the time coordinate; the resulting singularity at the black hole horizon is regulated by making the geometry slightly complex. Here, we consider generalizations of the double-cone geometry which include the Lorentzian cosmology that sits between the event horizon and the black hole singularity. We analyze this in two and three dimensions, where the cosmology has compact spatial sections and big bang/crunch singularities. These singularities are regulated in the same way by slightly complexifying the metric. We show that this is possible while satisfying the Kontsevich-Segal criterion, implying that these geometries can be interpreted as perturbatively stable saddle points in general relativity. This procedure leads to a novel description of the cosmology in terms of standard observables in the dual boundary CFT. In three dimensions, the cosmological solution gives a new contribution to the two-point function of the density of states in the boundary CFT. Unlike the usual double cone, it describes correlations between black hole microstates with different masses, and in a limit describes correlations between the statistics of heavy states and states near the BTZ threshold.
DOI: 10.1007/JHEP10(2024)184
Source: https://link.springer.com/article/10.1007/JHEP10(2024)184