Researchers have utilized observations from the Event Horizon Telescope (EHT) and the GRAVITY instrument to set limits on the parameters of ModMax black holes, a theoretical model incorporating nonlinearities in electromagnetism. The study focused on how the total dyonic charge (Q) and a nonlinearity parameter (v) affect the event horizon radius, photon sphere, and shadow size of a black hole. It was found that an increase in Q decreases these radii, while an increase in v shifts them towards the values predicted by the Schwarzschild metric.

To derive these constraints, a Markov Chain Monte Carlo (MCMC) analysis was performed using EHT shadow measurements of M87* and Sgr A*, along with mass and distance data. The results established upper limits for the ModMax parameters at a 95% credible level: Q < 0.391 and v < 4.153. This work also investigated the properties of a Novikov-Thorne thin accretion disk around these black holes, simulating images using backward ray tracing.

The simulations revealed that the observed flux from the accretion disk increases with Q, while an increase in v produces a slight decrease in disk brightness. These findings demonstrate the influence of ModMax parameters on the black hole shadow and accretion disk emission, thereby providing key observational constraints for charge and nonlinearity within this theoretical model. These results are significant for understanding gravity in extreme regimes and for the development of theories beyond general relativity.