Spacetime measurements with the photon ring
Why this work is in the frame
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Bibliographic record
Abstract
We explore the universal symmetries of the black hole photon ring in a wide range of non-Kerr spacetimes, including the Kerr-Newman, Kerr-Sen, Kerr-Bardeen, and Kerr-Hayward metrics. The demagnification exponent ($\ensuremath{\gamma}$) controls the size and flux scaling of higher-order images, which appear in the photon ring, the time delay ($\ensuremath{\tau}$) determines the timing of their appearance, and the rotation parameter ($\ensuremath{\delta}$) relates their relative orientations on the image plane. Our investigation reveals that these critical parameters respond distinctly to variations in black hole spin, generalized charge, and observer inclination, establishing them as complementary probes of spacetime geometry: $\ensuremath{\gamma}$ is predominantly influenced by charge and spin, $\ensuremath{\tau}$ is strongly affected by inclination, especially for near-extremal black holes, and $\ensuremath{\delta}$ is highly sensitive to spin. Notably, we find that the time delay provides an independent constraint on shadow size for polar observers, while the rotation parameter facilitates metric-independent spin measurements. Specifically, for Kerr black holes, the total variation in $\ensuremath{\gamma}$, $\ensuremath{\tau}$, and $\ensuremath{\delta}$ across all possible inclinations and spins is $\ensuremath{\lesssim}20%$, $\ensuremath{\lesssim}10%$, and $\ensuremath{\lesssim}60%$, respectively. By contrast, the Kerr shadow radius varies by only $\ensuremath{\lesssim}8%$. A future joint measurement of these critical parameters---along with the black hole shadow size---will enable precise spacetime characterization, including measurements of the spin, inclination, and generalized charge.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.003 |
| 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