A Study of Black Holes in $F(R)-$ModMax Gravity: Gravitational Lensing and Constraints from EHT Observations

The study of astrophysical phenomena like black hole shadows is an effective approach to properly understand the modified gravity and explore its validity. Motivated by recent astrophysical observations, we consider a black hole (BH) in $F(R)-$ModMax gravity and study the optical features such as the shadow's geometrical shape, energy emission rate, and deflection of light. More specifically, we show how the variation of the model parameters imprints specific signatures on these optical quantities. In the following, we consider such black holes as supermassive BHs and evaluate the parameters of the model with shadow size estimates done by the observations of M87* from the Event Horizon Telescope (EHT). According to our findings, the parameter $f_{R_{0}}$ plays an effective role in having results consistent with the EHT data such that the resulting shadow of AdS black holes in $F(R)-$ModMax gravity agrees with the observational data for $f_{R_{0}}<-1$. However, for dS black holes, a consistent result is observed for $f_{R_{0}}>-1$.