The future ability to test theories of gravity with black-hole shadows

TL;DR

The paper assesses how distinctly black-hole shadows from non-Kerr spacetimes can appear in horizon-scale images by combining 3D GRMHD MAD accretion simulations with horizon-penetrating KRZ spacetimes and GRRT rendering, then quantifying image differences with mismatch metrics. It finds that future VLBI missions ngEHT and BHEX can separate a broad class of KRZ deviations from Kerr when image mismatches exceed a few percent, implying percent-level image fidelity suffices to constrain strong-field gravity theories. The work emphasizes a generic, model-agnostic approach to testing GR in the strong-field regime and discusses robustness to different accretion states and electron-temperature prescriptions, while noting degeneracies that require additional observables (time variability, polarization, RM, etc.) or improved baselines. Overall, the study provides a framework showing that planned horizon-scale imaging can meaningfully test gravity near black holes, with specific mismatch thresholds guiding observational capabilities and instrument design.

Abstract

The horizon-scale images of supermassive black holes (BHs) by the Event Horizon Telescope Collaboration (EHT) have provided new opportunities to test general relativity and other theories of gravity. In view of future projects, such as the next-generation Event Horizon Telescope (ngEHT) and the Black-Hole Explorer (BHEX), having the potential of enhancing our ability to probe extreme gravity, it is natural to ask: \textit{how much can two black-hole images differ?} To address this question and assess the ability of these projects to test theories of gravity with black-hole shadows, we use general-relativistic magnetohydrodynamic and radiative-transfer simulations to investigate the images of a wide class of accreting BHs deviating from the Kerr solution. By measuring the mismatch between images of different BHs we show that future missions will be able to distinguish a large class of BHs solutions from the Kerr solution when the mismatch in the images exceeds values between $2\%$ and $5\%$ depending on the image-comparison metric considered. These results indicate future horizon-scale imaging with percent-level image fidelity can place meaningful observational constraints on deviations from the Kerr metric and thereby test strong-field predictions of general relativity.

Figures (15)

• Figure 1: Volume rendering image for Kerr and KRZ [1.0,1.0] BHs. Visualisation of the magnetic-field lines and volume rendering of the magnetisation $\sigma$ at $t=10,\!000 \, M$ for a GRMHD simulation of an accretion onto a Kerr BH with $a_0=1=a_1$ (left panel) or a KRZ BH (right). Shown on the top left of the two panels is reported a large-scale view.
• Figure 2: $\sigma$ Contours for Kerr and KRZ BHs.$\sigma=1.0$ contours for simulations onto a Kerr BH (black) and three representative KRZ BHs (blue, green, and red). The values refer to data that is azimuthally- and time-averaged ($t=8,\!000-10,\!000 \, M$). The jet region is described by $\sigma \geq 1$, while the disc region has $\sigma \ll 1$.
• Figure 3: $230\,{\rm GHz}$ time-averaged images: Kerr vs. KRZ BHs. Time-averaged ($t=8,\!000-10,\!000\,M$) intensity images at $230\,{\rm GHz}$ of accretion flows onto a Kerr BH (left column) and onto three representative Kerr BHs (second to fourth column). While the top row reports the data from the simulation, the bottom one show images using a circular Gaussian beam with a full width at half maximum (FWHM) of $20\,\mu{\rm as}$. The inclination angle is $i=30^\circ$, the BH spin is pointing upwards, and the disc rotating counter-clock wise.
• Figure 4: Intensity profiles along $y=0$ for Kerr and KRZ BHs. One-dimensional cuts at $y=0$ of the intensities reported in Fig. \ref{['fig:grrt']} for the four BHs considered.
• Figure 5: Image-Comparison metrics as a function of beam size.Left panel: Image-comparison metric in terms of the "mismatch" $1-{\rm nCCC}$ for different beam sizes and KRZ BHs. The various colour-shaded regions show the variations of the mismatch between a Kerr BH and KRZ BH with properties set by the given colormap. Reported with vertical lines are the present EHT resolutions and the expected ones for ngEHT and BHEX, while shown with different symbols are the mismatches corresponding to the three KRZ BHs reported in Figs. \ref{['fig:grrt']} and \ref{['fig:cross-cut']}. Right panel: The same as on the left but for the DSSIM image-comparison metric.