Possible physical realizations of the Tolman VII solution
Bibliographic record
Abstract
The Tolman VII solution for a static perfect fluid sphere to the Einstein equations is reexamined, and a closed form class of equations of state (EOSs) is deduced for the first time. These EOSs allow further analysis to be carried out, leading to a viable model for compact stars with arbitrary boundary mass density to be obtained. Explicit application of causality conditions places further constraints on the model, and recent observations of masses and radii of neutron stars prove to be within the predictions of the model. The adiabatic index predicted is $\ensuremath{\gamma}\ensuremath{\ge}2$, but self-bound crust solutions are not excluded if we allow for higher polytropic indices in the crustal regions of the star. The solution is also shown to obey known stability criteria often used in modeling such stars. It is argued that this solution provides realistic limits on models of compact stars, maybe even independently of the type of EOS, since most of the EOSs usually considered do show a quadratic density falloff to first order, and this solution is the unique exact solution that has this property.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".