Chaotic behavior in a charged three-body self-gravitating system
Bibliographic record
Abstract
We investigate the equal-mass three-body charged system in general relativistic lineal gravity. The electric properties of the charged particles along with the gravitational self-attraction of the bodies introduce features that do not have a nonrelativistic counterpart. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. We consider various combinations of charges and 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 are regions of quasiperiodicity while the latter is a region of chaos. When the charge configuration is repulsive the amount of chaos is enhanced relative to that of the neutral case (leading to Kolmogorov–Arnold–Moser breakdown), whereas the chaos is only enhanced throughout a band between the annulus and pretzel regions with a significant development of pretzel areas for attractive configurations when two charges have opposite signs. We find a new class of chaotic orbits that are of hourglass shape in the hexagonal representation of the three-body motion.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".