Shadow of F(R)-Euler–Heisenberg black hole and constraints from EHT observations

Abstract

This study investigates the optical properties of a static, spherically symmetric, electrically charged black hole in $f\left(R\right)$ gravity, coupled with Euler–Heisenberg ($\mathrm{EH}$) nonlinear electrodynamics (NLED). By analyzing photon trajectories in this background, we demonstrate how the model parameters influence light propagation, leading to broader ranges for both lensed paths and photon rings. We identify parameter regions that allow for physically consistent black hole shadows, characterized by a photon sphere located outside the event horizon and a shadow forming beyond it. These viable regions expand with increasing electric charge and $f_{R_0}$, highlighting the interplay between gravitational and electromagnetic effects. Constraining the model using Event Horizon Telescope (EHT) observations of M87*, we find that de Sitter (dS) black holes remain compatible with the data, whereas anti-de Sitter (AdS) solutions are disfavored under low charge and $f_{R_0}>-1$. Finally, our analysis of the energy emission rate shows that higher electric charge enhances black hole evaporation, while stronger NLED effects and larger $f_{R_0}$ values suppress it.