Gravitational lensing and shadows in the toron solution of Einstein’s equations using ray tracing methods
Bibliographic record
Abstract
We present a numerical and analytical study of the so-called ``toron'' solution of the stationary axisymmetric Einstein equations in vacuum expressed in terms of elliptic functions. The asymptotic behavior of this solution coincides with the one of the Newman-Unti-Tamburino (NUT) solution, i.e., it has a ``gravimagnetic'' mass known as the NUT parameter while the ordinary mass vanishes. The physical properties of this spacetime are studied via ray tracing. The results are compared to known geodesic flows in Schwarzschild, Kerr, and NUT spacetimes to discuss similarities and differences, with a particular emphasis on the comparison of NUT and toron spacetimes.
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How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gpt | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | low |
| grok | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | low |
| opus | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | medium |
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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, unvalidatedLabeled directly by 3 models reading the full record.
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".