Black hole photon ring beyond General Relativity: an integrable parametrization
Bibliographic record
Abstract
Abstract In recent years, the shape of the photon ring in black holes images has been argued to provide a sharp test of the Kerr hypothesis for future black hole imaging missions. In this work, we confront this proposal to beyond Kerr geometries and investigate the degeneracy in the estimations of the black hole parameters using the circlipse shape proposed by Gralla and Lupsasca. To that end, we consider a model-independent parametrization of the deviations to the Kerr black hole geometry, dubbed Kerr off shell (KOS), which preserves the fundamental symmetry structure of Kerr known as the Killing tower. Besides exhibiting a Killing tensor and thus a Carter-like constant, all the representants of this family also possess a Killing-Yano tensor and are of Petrov type D. The allowed deviations to Kerr, selected by the symmetry, are encoded in two free functions which depend respectively on the radial and polar angle coordinates. Using the symmetries, we provide an analytic study of the radial and polar motion of photon trajectories generating the critical curve, to which the subrings composing the photon ring converge. This allows us to derive a ready-to-use closed formula for the parametric critical curve in term of the free functions parametrizing the deviations to Kerr. Using this result, we confront the circlipse fitting function to four examples of Kerr-like objects and we show that it admits a high degree of degeneracy. At a given inclination, the same circlipse can fit both a Kerr black hole of a given mass and spin (M,a) or a modified rotating black hole with different mass and spin parameters (M,a) and a new parameter α. Therefore, future tests of the Kerr hypothesis could be achieved only provided one can measure independently the mass and spin of the black hole to break this degeneracy.
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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 | 0.001 |
| 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 | 0.002 |
| 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".