On the Evolution of Relativistic Dust in Schwarzschild–de Sitter and Schwarzschild–Anti‐de Sitter Spacetimes. Part I: The Vanishing Mass Case
Why this work is in the frame
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Bibliographic record
Abstract
ABSTRACT Given that relativistic density and velocity propagate at the same speed, the Cauchy problem with smooth and compactly supported initial data for relativistic dust in Schwarzschild–de Sitter (SdS) and Schwarzschild–anti‐de Sitter (SAdS) spacetimes without black hole has been investigated using the characteristic method. Based on the explicit solution formulas under the spherically symmetric assumption, a precise classification of the initial data is provided, elucidating whether the classical solution for relativistic dust will persist globally or encounter a finite‐time blowup. Moreover, the paper offers a further analysis of the exact blowup phenomenon, including detailed insights into the blowup rate related to the blowup time.
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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 it