How much chaos can be generated by gravitational collapse before reaching the Planck scale?
Abstract
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.
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BibTeX
@misc{brizuela2026much,
title = {{How much chaos can be generated by gravitational collapse before reaching the Planck scale?}},
author = {David Brizuela and Sara F. Uria and Edward Wilson-Ewing},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11570},
eprint = {2609.11570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11570},
}
RIS
TY - UNPB
TI - How much chaos can be generated by gravitational collapse before reaching the Planck scale?
AU - David Brizuela
AU - Sara F. Uria
AU - Edward Wilson-Ewing
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11570
UR - https://arxiv.org/abs/2609.11570
AB - 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.
ER -