Horizon-Scale Imaging Tests of Kerr

Event Horizon Telescope (EHT) visibilities support a persistent horizon-scale ring in M87* and a roughly $50\,\mu\mathrm{as}$ ring-like structure in Sgr A*. After calibrating the observed bright ring with simulations and external mass-to-distance information, the angular scale is consistent with Kerr at roughly the present ten-percent level. At the evidence cutoff of 2026-08-20, this is a meaningful strong-field consistency test and constrains selected parametric metrics. It is not a model-independent measurement of Kerr, a precise spin determination from ring size, or a resolved universal photon ring.

Helpful background. Horizon-Scale Imaging Tests develops interferometric observables, the bright-ring versus critical-curve distinction, plasma calibration, and the logic of parametric metric tests. This record weighs current sources, epochs, and public products.

From a visibility to a metric statement

Interferometers measure complex visibilities at sampled baselines, not images. An image is a regularized posterior product; a fitted ring is a lower-dimensional description; the geometric critical curve is a property of null geodesics. Moving between those levels requires calibration, scattering and variability treatment, and a radiative-transfer model. The distinction prevents a common category error: an observed bright-ring diameter is not automatically the photon-ring diameter.

Five axes delimit the claim: source, epoch, frequency, and polarization product; visibility- or image-domain statistic; external mass-to-distance prior and covariance; calibration, variability, scattering, imaging algorithm, and GRMHD electron model; and the tested metric family with regularity cuts, spin, inclination, and coverage. Bounds in one parametric family need not apply to a different family that maps nuisance parameters differently.

Assessment at 2026-08-20	Meaning
Question status	Partially resolved
Evidence status	Supported
Confidence	Moderate because scale persistence is persuasive while metric inference remains simulation- and family-dependent
Domain	Public M87* 2017, 2018, and 2021 and Sgr A* 2017 EHT products, with declared mass-to-distance, plasma, variability, scattering, and metric priors
What could change the conclusion	A calibrated imaging release, cross-method analysis, or decisive plasma-systematics result

Entry project: test a ring measurement before a metric test

This route suits students who enjoy inverse problems, Fourier analysis, and statistical model checking. Prepare by deriving the visibility of a simple circular brightness distribution and explaining closure quantities. A small geometric fit to calibrated public data can run on a laptop; a complete imaging survey or GRMHD model library is a group project with substantially larger computational and calibration demands.

Begin with EHT Collaboration 2022, Sgr A* Paper III, §§5–9, extracting the synthetic-data tests and variability treatment. Use the official calibrated Sgr A* product EHT 2022-D02-01, retaining its day, frequency band, station selection, and uncertainty fields. Fit one explicitly defined geometric brightness model to a restricted data selection, and reproduce its Fourier-domain prediction on the measured baselines. This is a model-fitting baseline; it is not a recreation of the collaboration’s full imaging analysis.

Deliver the fit, residuals, and a synthetic-data recovery test using the same Fourier coverage. Compare diameter estimates after changing one brightness assumption or holding out one scan. Read EHT Collaboration 2022, Paper VI, §§2–3 only after that exercise, and write down the additional calibration and mass-to-distance information needed to turn a bright-ring scale into a metric constraint.

A candidate extension, with novelty unchecked, is a controlled comparison of diameter bias for two emission profiles at fixed underlying geometry and realistic sampling. Stop if variability or station-dependent residuals exceed the model’s noise description, or if changing priors determines the apparent precision. Pivot to synthetic data when the observational likelihood is not under control. Consult an interferometry specialist before combining closure quantities with dependent visibility amplitudes. A stable geometric fit does not establish that the fitted ring is a resolved photon subring.

What present images and visibilities establish

For Sgr A*, multiple algorithms, synthetic-data campaigns, variability mitigation, and scattering tests recover a ring-like structure of about $50\,\mu\mathrm{as}$ EHT Collaboration 2022, Paper III, §§ 5–9 and ring-diameter tables. Rapid intrinsic variability and sparse Fourier coverage broaden the morphology, but the scale is not an artifact of one imaging code.

Paper VI converts that scale into metric tests. It calibrates the bright-ring to shadow relation with simulations, combines the result with mass-to-distance information, and constrains several deviation metrics subject to their regularity domains EHT Collaboration 2022, Paper VI, §§ 2–3 and Figs. 2–13. The result is consistency with Kerr at the present calibration precision. Vagnozzi and collaborators analyze related observables across alternative metrics and recover useful but visibly family-dependent bounds Vagnozzi et al. 2023, §§ 2–5 and comparison tables.

M87* adds time. The 2018 data preserve a similar ring diameter while the brightness orientation changes EHT Collaboration 2024, §§ 5–9 and Figs. 9–17. Joint 2017, 2018, and 2021 intensity and polarization analyses find further plasma-state changes around a persistent scale EHT Collaboration 2025, §§ 4–7. Cross-epoch stability is evidence for a gravitationally set scale; cross-epoch morphology change is evidence against treating every bright feature as geometry.

Results and open questions at 2026-08-20

Claim or evidence	What it supports	What it does not establish
Sgr A* multi-algorithm ring recovery	A robust horizon-scale characteristic size	A unique image or variability-free morphology
Simulation-calibrated Sgr A* metric tests	Kerr consistency and bounds in named metric families	Model-independent geometry or precise spin
Independent alternative-metric synthesis	Reproducible scale-level constraints and family dependence	Independent visibility reduction
M87* 2017–2018 scale persistence	Stable lensing/accretion scale across epochs	Isolation of a narrow geometric subring
M87* 2017–2021 polarization variability	Plasma morphology is time dependent	Failure of Kerr
Public total-intensity and polarization products	Inspectable input boundary across sources and epochs	One archive reproducing every published posterior

The cross-epoch observations and synthetic-data validation carry more weight than agreement among reconstructed images sharing data and priors. Reusing an EHT summary likelihood is valuable, but only partially independent.

Strongest competing interpretations

The Kerr-consistency interpretation emphasizes dimensional economy. Given independent $M/D$, the observed angular scale falls where Kerr lensing and plausible accretion flows place it. Its persistence while brightness rotates is exactly what one expects if gravity fixes the scale and turbulent plasma paints the ring.

The competing interpretation is not that the ring is spurious. It is that present data constrain a degenerate combination of metric, inclination, emission profile, electron heating, scattering, variability, and reconstruction. Many regular non-Kerr metrics can mimic the same characteristic diameter after nuisance adjustment. Vagnozzi et al.’s cross-family results show that a quoted deformation bound belongs to its metric parameterization. The current ngEHT review likewise separates the broad observed emission ring from the narrow higher-order photon ring that would be more geometric Ayzenberg et al. 2025, §§ 2 and 5.2.1–5.2.2.

Counterexamples, null results, and failed routes

The observed changes in brightness and polarization at nearly fixed ring scale are the strongest adverse evidence against reading an image as a stationary metric map. They do not undermine the characteristic-scale test; they establish the size of the plasma nuisance problem. A method that fits one epoch perfectly but fails held-out epochs has learned a source state, not necessarily geometry.

No current public product resolves the narrow universal photon-ring substructure required for a substantially cleaner geometric inference. Treating the broad emission ring as that subring is therefore a failed route. Likewise, taking the best reconstructed image as raw data discards algorithmic uncertainty. The relevant likelihood begins in the visibility domain, with array coverage and calibration included.

What the ten-percent statement means

“Within about ten percent” combines statistical and calibration uncertainties in the mapping from observed emission diameter to a spacetime scale. It is not a ten-percent measurement of every metric coefficient. A deformation may change the critical curve little while changing other observables strongly, or vice versa. Metric pathologies can also make portions of a nominal parameter prior physically inadmissible.

Spin illustrates the problem. For much of the allowed Kerr parameter space, shadow diameter depends weakly on spin compared with plasma and inclination uncertainties. Ring size alone therefore cannot yield a precise spin even when it agrees with Kerr. Polarization, dynamics, and future subring or multi-frequency information may help only through a joint, calibrated likelihood.

What would change the assessment

A decisive advance would blind independent teams to injected source identity and pass Kerr and regular non-Kerr metrics through a shared, preregistered plasma and variability ensemble with real array coverage. Visibility-domain coverage and false-exclusion rates should be measured before applying unchanged pipelines to all 2017, 2018, and 2021 releases. Held-out epochs would test whether geometry transfers when plasma state changes.

Confidence would rise if a metric-sensitive observable remains stable across epochs, frequencies, plasma libraries, and independent codes, with systematic error below the predicted deviation. A resolved higher-order subring would be especially valuable. Confidence would fall if Kerr bounds disappear under reasonable GRMHD or metric-family changes, or if synthetic non-Kerr injections are repeatedly misclassified as Kerr.

Research checklist

• Start from a named visibility product; distinguish calibrated data, reconstructed image, fitted ring, and geometric critical curve.
• Pin station/network metadata, calibration, scattering kernel, variability segmentation, and imaging or forward-model commit.
• State the $M/D$ prior and covariance, GRMHD library, electron prescription, frequency, inclination, and polarization treatment.
• Define the metric family, regularity domain, spin prior, and coverage convention before fitting.
• Validate on synthetic Kerr and non-Kerr injections with real Fourier coverage; report false exclusions and held-out epochs.
• Compare several visibility-domain and image-domain methods without treating their shared data as independent experiments.
• Report how ring-to-critical-curve calibration changes across plasma models and epochs.
• No independent computational rerun was performed for this assessment; the products below define the bounded reproduction and blind-test prescription.

Source and data map

Sgr A* Papers III and VI provide the primary morphology and metric inference. Vagnozzi et al. supply a partially independent alternative-metric synthesis. The 2024 and 2025 M87* papers provide cross-epoch intensity and polarization evidence. Ayzenberg et al. supply current systematic and ngEHT context.

The public product boundary includes M87* 2019-D01-01 DOI 10.25739/g85n-f134, the 2019-D01-02 imaging repository, Sgr A* 2022-D02-01 DOI 10.25739/m140-ct59, M87* 2024-D01-01 DOI 10.25739/epm5-r371, 2025-D01-01 DOI 10.25739/v7hh-6244, and 2025-D02-01 DOI 10.25739/vddx-w132. Product 2026-D01-01 is identified by CyVerse path EHTC_M87-2018+2021_Jul2026; the official inventory exposed no DOI at the cutoff, so none is guessed.

Return to the seminar

Record this page’s worksheet, return to Case 4 in the Research Seminar, then continue to Case 5 — What island calculations establish. Read its seminar instructions before treating it as a reproduction candidate.

References

• Ayzenberg, D., et al. “Fundamental physics opportunities with the next-generation Event Horizon Telescope.” Living Reviews in Relativity 28, 1 (2025). DOI.
• Event Horizon Telescope Collaboration. “First Sagittarius A* EHT Results: Calibrated Data.” Data product 2022-D02-01 (2022). DOI.
• Event Horizon Telescope Collaboration. “First Sagittarius A* Event Horizon Telescope results. III. Imaging of the Galactic Center supermassive black hole.” Astrophysical Journal Letters 930, L14 (2022). DOI.
• Event Horizon Telescope Collaboration. “First Sagittarius A* Event Horizon Telescope results. VI. Testing the black hole metric.” Astrophysical Journal Letters 930, L17 (2022). DOI.
• Event Horizon Telescope Collaboration. “Horizon-scale variability of M87* from 2017–2021 EHT observations.” Astronomy & Astrophysics 704, A91 (2025). DOI.
• Event Horizon Telescope Collaboration. “The persistent shadow of the supermassive black hole of M87. I. Observations, calibration, imaging, and analysis.” Astronomy & Astrophysics 681, A79 (2024). DOI.
• Vagnozzi, S., et al. “Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A*.” Classical and Quantum Gravity 40, 165007 (2023). DOI.