Chaos in a three-body self-gravitating cosmological spacetime
Bibliographic record
Abstract
We investigate the equal-mass three-body system in general relativistic lineal gravity in the presence of a cosmological constant $\ensuremath{\Lambda}$. The cosmological vacuum energy introduces features that do not have a nonrelativistic counterpart, inducing an expansion/contraction of space-time that competes with the gravitational self-attraction of the bodies. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. As for the system with $\ensuremath{\Lambda}=0$, we find that the structure of the phase space yields a rich variety of interesting dynamics that can be divided into three distinct regions: annulus, pretzel, and chaotic; the first two being regions of quasiperiodicity while the latter is a region of chaos. However, unlike the $\ensuremath{\Lambda}=0$ case, we find that a negative cosmological constant considerably diminishes the amount of chaos in the system, even beyond that of the $\ensuremath{\Lambda}=0$ nonrelativistic system. By contrast, a positive cosmological constant considerably enhances the amount of chaos, typically leading to KAM (Kolmogorov-Arnold-Moser) breakdown.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".