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Prospects for Improving the Theoretical Uncertainty for Tests of General Relativity with the EHT

T0 review · 2 major / 2 minor · reviewed 2026-07-01 · grok-4.3

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Pith's one-line read The theoretical uncertainty in the bright ring to black hole shadow size relationship can be reduced substantially with future EHT observations at 345 GHz and targeted constraints.

desk verdict A broad simulation campaign that ranks practical ways to tighten the ring-shadow calibration, but the gains rest on how well the models match real flows. read the letter →

arxiv 2606.30753 v1 pith:XWDJMVHS submitted 2026-06-29 astro-ph.HE gr-qc

Lia Medeiros , George N. Wong , Feryal Ozel This is my paper · ORCID
classification astro-ph.HEgr-qc
keywords blackholeshadowEventHorizonTelescopegeneralrelativitytestsM87SgrA*accretionflowmodelsimagereconstructiontheoreticaluncertainty
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper establishes a calibration between the size of the bright ring seen in simulated black hole images and the size of the analytic black hole shadow. This calibration supports mass measurements from EHT data and, when masses are known independently, tests of general relativity. The authors show that the uncertainty in the calibration shrinks when observations move to 345 GHz, when geometric constraints such as ring width from the PRIMO algorithm are applied, when the black hole spin axis is aligned with the observed jet, and when the accretion flow is modeled as a magnetically arrested configuration. They further project that the uncertainty will continue to fall as more observations accumulate and identify dwell-time filtering as a method to improve the calibration precision.

What carries the argument

The calibrated relationship between bright ring size in simulated images and analytic black hole shadow size, used to convert observed ring diameters into mass or GR-test inferences.

What would settle it

A set of real 345 GHz EHT images, after application of the listed geometric and astrophysical constraints, that show ring-to-shadow discrepancies lying outside the reduced uncertainty range reported in the simulations.

Watch

Extended reading notes

Core claim

The relationship between the observed bright ring diameter and the analytic black hole shadow diameter, calibrated across a large suite of high-resolution general relativistic magnetohydrodynamic simulations with varied accretion-flow models and initial conditions, exhibits a theoretical uncertainty that decreases relative to current levels under higher-frequency observations, geometric image constraints, astrophysical alignment constraints, and the assumption of a magnetically arrested disk. The uncertainty is also projected to decrease further with additional observations in subsequent years when dwell-time filtering is used to evaluate persistence of geometric measurements.

Load-bearing premise

The simulated images with varied accretion-flow models faithfully reproduce the ring-shadow relationship that will appear in actual EHT observations of M87 and Sgr A*.

Editorial extensions

If this is right

  • Observing at 345 GHz reduces the uncertainty in the ring-shadow relationship compared with existing measurements.
  • Applying geometric constraints such as ring width from the PRIMO algorithm further reduces the uncertainty.
  • Incorporating the constraint that the M87 black hole spin axis aligns with the large-scale jet reduces the uncertainty.
  • Adopting the assumption of a magnetically arrested accretion flow configuration reduces the uncertainty.
  • The uncertainty is expected to decrease as more observations are obtained over time, with dwell-time filtering providing an additional improvement path.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the reduced uncertainty holds, independent mass measurements combined with EHT ring sizes could yield tighter bounds on deviations from the Kerr metric.
  • Dwell-time filtering could be tested on existing multi-epoch EHT data sets to check whether it improves calibration stability before new observations arrive.
  • The same constraint strategy might be adapted to other compact-object imaging efforts that rely on ring or shadow features.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper calibrates the relationship between the bright ring size in simulated EHT images and the analytic black hole shadow size using a large library of high-resolution GRMHD simulations that vary accretion-flow modeling approaches, system parameters, and initial conditions. It claims that the theoretical uncertainty in this calibration (relevant for mass measurements and GR tests) can be reduced substantially relative to current values by (i) observing at 345 GHz, (ii) applying geometric constraints such as PRIMO ring-width inference, (iii) imposing astrophysical constraints such as M87 spin-jet alignment, and (iv) restricting to magnetically arrested disk (MAD) models; it further projects continued improvement with additional epochs and dwell-time filtering.

Significance. If the simulation-based uncertainty reductions are representative of real EHT data, the work would directly improve the precision of shadow-based GR tests and mass measurements for M87* and Sgr A*. The broad simulation campaign spanning multiple modeling approaches is a methodological strength that allows an empirical rather than purely analytic estimate of scatter.

major comments (2)
  1. [simulation campaign description and results sections] The central claim that the quoted uncertainty reductions apply to real observations rests on the assumption that the simulation library brackets the ring-shadow relationship present in actual M87/Sgr A* data. The manuscript does not include explicit tests or discussion of additional physics (two-temperature effects, non-thermal electron distributions, or time-dependent reconnection) known to alter image morphology in EHT-relevant regimes; without such tests the projected reductions remain conditional on the chosen GRMHD setups.
  2. [results on uncertainty reduction] The quantitative uncertainty values before and after each constraint (345 GHz, PRIMO, jet alignment, MAD) are presented only as relative decreases; the manuscript should report the absolute calibrated mean and scatter (with error budgets) for each case so that the improvement can be assessed against the existing measurement baseline.
minor comments (2)
  1. Notation for the ring and shadow radii should be defined once at first use and used consistently; occasional switches between descriptive phrases and symbols reduce readability.
  2. [future observations discussion] The dwell-time filtering proposal would benefit from a short quantitative example showing how persistence over multiple epochs reduces scatter in the calibration sample.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major comment below, indicating where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [simulation campaign description and results sections] The central claim that the quoted uncertainty reductions apply to real observations rests on the assumption that the simulation library brackets the ring-shadow relationship present in actual M87/Sgr A* data. The manuscript does not include explicit tests or discussion of additional physics (two-temperature effects, non-thermal electron distributions, or time-dependent reconnection) known to alter image morphology in EHT-relevant regimes; without such tests the projected reductions remain conditional on the chosen GRMHD setups.

    Authors: We agree that the uncertainty reductions we report are conditional on the GRMHD setups in our library. While the campaign spans multiple accretion-flow modeling approaches, initial conditions, and system parameters, it does not incorporate two-temperature effects, non-thermal electron distributions, or time-dependent reconnection. In the revised manuscript we will add explicit discussion of these limitations in the methods and conclusions sections, stating that the quoted reductions apply within the context of the current simulation suite and that additional physics could modify the calibration. We will also insert a clarifying sentence in the abstract. revision: partial

  2. Referee: [results on uncertainty reduction] The quantitative uncertainty values before and after each constraint (345 GHz, PRIMO, jet alignment, MAD) are presented only as relative decreases; the manuscript should report the absolute calibrated mean and scatter (with error budgets) for each case so that the improvement can be assessed against the existing measurement baseline.

    Authors: We appreciate this recommendation. The revised manuscript will include a new table (and updated figures) reporting the absolute mean ring-to-shadow ratio and the standard deviation (scatter) across the simulation ensemble for the baseline and each constrained case, together with the associated error budgets. This will enable direct comparison against the current EHT measurement baselines. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; calibration is independent of target claims

full rationale

The paper measures the ring-to-shadow size relationship directly from a library of high-resolution GRMHD simulations that vary accretion models, parameters, and initial conditions. This empirical calibration is performed first and independently; the subsequent claims about uncertainty reduction (via 345 GHz, PRIMO constraints, jet alignment, or MAD assumptions) are obtained by subsetting or filtering the same pre-existing library rather than by redefining the relationship in terms of the reductions themselves. No equation equates a derived quantity to its own input by construction, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation whose content is unverified. The derivation chain is therefore self-contained against the simulation benchmarks.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the fidelity of the simulation library and the applicability of the four listed constraints; no explicit free parameters or invented entities are named in the abstract.

free parameters (2)
  • accretion-flow modeling parameters
    Wide range of system parameters and initial conditions across different modeling approaches
  • geometric constraint parameters
    Ring width inference from PRIMO and similar algorithms
assumptions (2)
  • domain assumption Simulated images accurately capture the ring-shadow mapping present in real EHT data
    Calibration is performed entirely on simulations; transfer to observations is assumed.
  • domain assumption Spin axis of M87 is aligned or anti-aligned with the large-scale jet
    Listed as one of the constraints that reduces uncertainty.

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Cite this review

Pith. "Pith review of Prospects for Improving the Theoretical Uncertainty for Tests of General Relativity with the EHT." pith.science (2026). https://pith.science/paper/XWDJMVHS

@misc{pith2026260630753,
  author       = {Pith},
  title        = {Pith review of: Prospects for Improving the Theoretical Uncertainty for Tests of General Relativity with the EHT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XWDJMVHS}},
  note         = {Machine review of arXiv:2606.30753}
}
read the original abstract

We characterize the relationship between the size of the bright ring observed in simulated black hole images and the size of the analytic black hole shadow. Calibrating this relationship is crucial for mass measurements and, when independent mass measurements are available, for tests of general relativity using Event Horizon Telescope (EHT) images. We perform this calibration using a large set of high-resolution simulated images generated with different accretion-flow modeling approaches and spanning a wide range of system parameters and initial conditions. We show that the theoretical uncertainty in this relationship can be reduced significantly through future observations, improved imaging techniques, and the application of astrophysical or model-based constraints. In particular, the uncertainty decreases compared to existing measurements when (i) observing at 345 GHz, (ii) applying geometric image constraints, such as the ring width inference from the PRIMO image reconstruction algorithm, (iii) incorporating astrophysical constraints such as the black hole spin axis in M87 being aligned (or anti-aligned) with the large-scale jet observed at longer radio wavelengths, and (iv) assuming that the accretion flow can be described by a magnetically arrested field configuration. Finally, we quantify how the uncertainty is expected to decrease as additional observations are obtained in subsequent years and identify dwell-time filtering, i.e., evaluating the persistence of a geometric measurement over time, as a promising avenue for improving the precision of the calibration.

Figures

Figures reproduced from arXiv: 2606.30753 by the authors.

Figure 1
Figure 1. Example snapshots from the simulation libraries superimposed with the outputs from the CHARM feature extraction algorithm. The analytically calculated black hole shadow boundary is denoted by a dashed cyan curve and the median ring diameter from CHARM is denoted by a white dotted circle. The median ring width from CHARM is represented by two solid white circles (shown assuming that the width is symmetric about the m… view at source ↗
Figure 2
Figure 2. Correlation between the diameter calculated by CHARM for a 230 GHz image vs. the same image at 345 GHz for the M87 libraries. The contours show eight logarithmically spaced levels spanning over 2 orders of magnitude (each successive contour is just less than twice the value of its neighbor). The gray shaded region corresponds to the range of possible shadow sizes for all Kerr shadows. emission region, together with … view at source ↗
Figure 3
Figure 3. Fractional diameter difference (FDD, top panels) and width (bottom panels) from CHARM for Library A (left) and B (right) at both 230 GHz (magenta) and 345 GHz (blue) for both M87 and Sgr A∗ . The modified box-and-whisker plots show the central 68% (box) and 95% (whisker) ranges for the distributions. We also show the results of fitting a skewed Cauchy distribution as solid lines (color coded to match the histograms)… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Modified box and whisker plots comparing the distribution of the fractional diameter difference for both libraries at both wavelengths as a function of spin (x-axis) and the observer’s inclination (different colors) for the Sgr A∗ part of the libraries; the left column…
Figure 5
Figure 5. Figure 5: Comparison of the distribution of the fractional diameter difference for both M87 libraries at both wavelengths as a function of spin, magnetic flux (SANE/MAD), and the Rhigh parameter. For Library A (top row) the x-axis shows both the magnetic flux (SANE vs. MAD) as w…
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Distribution of FDD (top) and ring width (bottom) measurements for different mass accretion rates (different colors) at 230 GHz (left) and 345 GHz (right) for Library A as a function of spin and magnetic flux. Increasing the accretion rate consistently increases the me…
Figure 8
Figure 8. Figure 8: Dependence of the spread in FDD versus ac￾cretion rate for two “best-bet” models for the M87 accretion flow (based on total intensity, linear polarimetric, multiwave￾length, and jet power constraints Event Horizon Telescope Collaboration et al. 2021b). The images for t…
Figure 9
Figure 9. Figure 9: Distribution of FDD for different values of Rlow (different colors) at 230 GHz (left) and 345 GHz (right) for the M87 portion of Library B. Higher Rlow tends to result in higher and more variable FDD. spin, and on the Rhigh parameter for the M87 libraries. We show a si…
Figure 10
Figure 10. Figure 10: (top row) The distribution of width vs. FDD for the 230 GHz images for the M87 parts of both libraries. The contours are logarithmic and span two and a half orders of magnitude. The region of the parameter space that is consistent with the PRIMO constraint is highligh…
Figure 11
Figure 11. Figure 11: Filled histograms show the distribution of FDD measured from all snapshots across all simulations (identical to [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: Fractional variability of FDD across models in Libraries A (left) and B (middle, right). Each panel shows |x| plotted against |sx| for the FDD time series of each model at 230 GHz. Marker shape and color identify the model. Across both libraries, models with smaller m…
Figure 13
Figure 13. Figure 13: Comparison of FDD correlation times at 230 GHz and 345 GHz for MAD (left) and SANE (right) models from the high-cadence subset of Library B. Each point represents a single simulation, with the marker colors, fills, and shapes denoting spin, Rlow, and Rhigh. SANE model…
Figure 14
Figure 14. Figure 14: Effect of dwell-time-based filtering for a representative SANE model from Library B (spin a∗ = −0.5, Rlow = 10, Rhigh = 10). Left top: Time series of FDD at 230 GHz (magenta) and 345 GHz (blue). Left bottom: Normalized autocorrelation functions for both time series. T…
Figure 15
Figure 15. Figure 15: Stability of the inferred ring diameter as a function of diameter, accretion state, black hole spin, and observing frequency. Each panel shows the longest contiguous time interval over which the inferred ring diameter remains within ±1% of its value at the start of th…

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