A Universal Framework for Horizon-Scale Tests of Gravity with Black Hole Shadows

Abstract

In this Letter, we have developed a numerically efficient framework for evaluating parameters in metric theories of gravity, and applied it to constrain the horizon-scale magnetic field in the Kerr-Bertotti-Robinson (Kerr-BR) spacetime using the latest EHT observations. The method's adaptive ray-tracing strategy achieves near-linear computational efficiency without loss of numerical accuracy. Owing to this efficiency, the framework enables high precision shadow modeling at minimal computational cost and, for the first time, supports statistically robust inference of black hole parameters from horizon-scale observations for arbitrary stationary black holes. The above framework is applied to the recently obtained Kerr-BR black hole, an exact magnetized and rotating solution to the Einstein field equations. We have evaluated the horizon-scale magnetic fields of M87* and Sgr A*, with the latter showing a field strength of $93.3^{+14.7}_{-23.8}G$, consistent with the equipartition estimate of $71G$ from polarized ALMA observations, thereby supporting Einstein's gravity.

Figures (9)

• Figure 1: Schematic of the backward ray-tracing setup. A virtual observer at large distance defines the image plane $(x,y)$ with field of view $\alpha_{\rm fov}$. Each grid point $(m,n)$ corresponds to a photon integrated backward in time until it crosses the horizon or escapes to infinity. The purple curve is the apparent shadow contour obtained from the captured/escaping photon separator. The orange circle is a reference circle used for noncircular shadows; it does not coincide with the shadow but serves as a comparator to quantify size and deformation (e.g., via characteristic points $P_A,P_B,P_C,P_D$).
• Figure 2: Variation of the axial ratio $\mathcal{D}_s$ with the spin parameter $a/M$ for the Kerr black hole, extracted from images simulated at different pixel resolutions.
• Figure 3: Corner plot showing the one- and two-dimensional posterior probability distributions of the BH parameters for M87*, based on the three-epoch combined measurements from the EHT Collaboration EventHorizonTelescope:2025vum. The dashed lines indicate the $68\%$ CL, while the dot-dashed line marks the mean value of $\tilde{B}$.
• Figure 4: Corner plot showing the one- and two-dimensional posterior probability distributions of the BH parameters for Sgr A*, derived from the 2022 EHT observations EventHorizonTelescope:2022wkp within the Kerr-BR spacetime. The dashed lines indicate the $68\%$ CL, while the dot-dashed line marks the mean value of $\tilde{B}$.
• Figure 5: Schematic illustration of the shadow-area fraction $A_{\rm sh}$ for the Schwarzschild black hole.