发表机构
University of the Basque Country; University of New Brunswick（巴斯克大学; 新不伦瑞克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过香农熵、KL散度和傅里叶分析，量化了引力坍缩在经典区域至普朗克尺度产生的混沌，发现混沌特征不发达，不足以抹去初始信息，并刻画了Bianchi IX动力学的不变排斥子。
AI 中文摘要
根据Belinski-Khalatnikov-Lifshitz（BKL）猜想，广义相对论在奇点附近的动力学是高度混沌的。然而，由于广义相对论在奇点处失效，人们普遍预期需要更基础的理论（如量子引力）来描述具有大时空曲率区域的时空动力学。在缺乏被广泛接受的量子引力理论的情况下，量子效应究竟如何修改经典演化仍不清楚。采取保守的观点，本文研究了引力坍缩的经典动力学，从强场（尽管是经典的）情景开始，直到普朗克尺度，以量化在爱因斯坦方程可信期间产生的混沌量。具体而言，我们使用香农熵和Kullback-Leibler散度以及傅里叶分析，发现在达到普朗克尺度时，模型的混沌特征仍然相对不发达。这表明，至少在经典区域，混沌不足以抹去关于宇宙初始状态或反弹宇宙学中先前经典宇宙的所有信息。此外，我们还刻画了广义相对论中混沌Bianchi IX动力学的最终不变相空间分布，这为其不变排斥子提供了一种新的描述。
英文摘要
According to the Belinski-Khalatnikov-Lifshitz (BKL) conjecture the dynamics of general relativity near singularities is highly chaotic. However, since general relativity breaks down at singularities, it is generally expected that a more fundamental theory, such as quantum gravity, is needed to describe the spacetime dynamics in regions with large spacetime curvature. In the absence of a widely accepted theory of quantum gravity, it remains unclear how exactly quantum effects may modify the classical evolution. Taking a conservative point of view, in this paper we study the classical dynamics of a gravitational collapse, starting from a strong-field (though classical) scenario up to the Planck scale to quantify how much chaos is generated during the time the Einstein equations can be trusted. Specifically, we use the Shannon entropy and Kullback-Leibler divergence, as well as Fourier analysis, to find that, when the Planck scale is reached, the chaotic features of the model remain relatively underdeveloped. This suggests that, at least during the classical regime, chaos is not strong enough to erase all information about the initial state of the universe, or about a previous classical universe in the context of bouncing cosmologies. In addition, we also characterize the final invariant phase-space distribution for the chaotic Bianchi IX dynamics in general relativity, which provides a novel description of its invariant repeller.
