Wave-optical treatment of the shadow cast by a large gravitating sphere
Bibliographic record
Abstract
We study the shadow cast by a large gravitating sphere, similar to our Sun. For this, we consider the gravitational field produced by a static mass monopole within the first post-Newtonian approximation of the general theory of relativity. We study the propagation of a monochromatic electromagnetic wave in the vicinity of a large, opaque, gravitating sphere. To treat the opaque nature of the body and its physical size, we implement fully absorbing boundary conditions and develop a wave-optical treatment of the shadow formed by this object. Based on this approach, we demonstrate that the structure of the shadow is determined by the Schwarzschild radius of the body and its physical size. The shadow's boundary has the shape of a concave rotational hyperboloid bent inward due to the refractive properties of the curved spacetime. We show that there is no light in the shadow. However, even in the presence of gravity and related gravitational bending of photon trajectories there is the bright spot of Arago that is formed behind a perfectly spherical obscuration.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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, 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".