SciPost Submission Page
Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
by Gerben Oling, Juan F. Pedraza
Submission summary
| Authors (as registered SciPost users): | Gerben Oling |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2409.05836v2 (pdf) |
| Date accepted: | 2025-01-06 |
| Date submitted: | 2024-10-22 13:02 |
| Submitted by: | Oling, Gerben |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We demonstrate that the Carroll limit of general relativity coupled to matter captures the chaotic mixmaster dynamics of near-singularity limits. Zooming in on the behavior of general relativity close to spacelike singularities reveals rich and solvable ultra-local Belinski-Khalatnikov-Lifshitz (BKL) dynamics, which we show to be captured by a Carroll limit. Specifically, building on recent work on geometric Carroll expansions of general relativity, we establish that leading-order Carroll gravity, with suitable matter coupling, accurately describes well-known cosmological billiards behavior. Since the Carroll limit implements the ultra-local limit off shell, this opens up the door to a wide range of possible tractable applications, including spatially inhomogeneous setups and the emergence of spikes at late times. This further suggests that Carroll gravity, along with its subleading corrections, could serve as a valuable tool for studying deep infrared physics in AdS/CFT.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Editorial decision:
For Journal SciPost Physics Core: Publish
(status: Awaiting author acceptance of publication offer)
Reports on this Submission
Strengths
1. The manuscript has a good review of both BKL/mixmaster dynamics and the Carrollian limit in sections 2 and 3.
2. The presentation is clear, and the main conceptual point on the relationship between Carrollian and BKL physics is very elegant.
Weaknesses
1. Most of the paper seems to be review. The novel technical material is localized to a short section 4.
Report
I think this paper contains very interesting observations and deserves to be published. The impact would be greatly increased if the technology built up around the Carrollian limit allows for a technically sound and tractable framework for computing quantum and stringy corrections to BKL physics.
Requested changes
1. I think it would be useful, in the discussion, to make some comments on the exact relationship between the ultralocality of the BKL setup and the ultralocality of the Carrollian limit. Naively the physics behind the two regimes is very similar - when approaching a spacelike singularity, light simply does not have much time to propagate, so it makes sense that the c ->0 limit is relevant. It was unclear to me whether the authors are claiming that the physics of the Kasner/BKL regime really is equivalent to the Carrollian regime, and whether it's obvious that perturbative corrections in c would accurately capture realistic corrections to BKL behavior away from the ultralocal limit.
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
1. The paper shows an interesting connection between Carroll gravity and Kasner/mixmaster models used to study dynamics close to curvature singularities. The result for the mixmaster model is new and original.
2. Clear exposition, clear calculations.
3. Potential new applications to study near-singularity physics in AdS/CFT from the boundary by using Carroll symmetry.
Weaknesses
1. The progress is good, but somewhat limited. Sections 2 and 3 are essentially reviews, and section 4 contains some new results. For the Kasner geometries, this was long expected (but shown explicitly here), and for the mixmaster model, it is an honest new result.
2. The consequences of having a Carroll description of the mixmaster model remain a bit unclear. What did we now learn from this about BKL dynamics now? Some comments addressing this are in the outlook.
Report
I find the paper of good quality and with enough new material to recommend publication.
Requested changes
I think formula (2.13) is not quite correct. Are there squares missing over these one-forms?
Recommendation
Publish (meets expectations and criteria for this Journal)