Spherically symmetric charged (anti-)de Sitter black hole in $f(R,T)$ gravity coupled with nonlinear electrodynamics

Abstract

We investigate black hole solutions in quadratic $f(R,T)=R+kT^2$ gravity coupled with nonlinear electrodynamics $\mathcal{L}(F)=α- F/(4π) + γF^2$. Solving the field equations yields an exact magnetically charged (anti-)de Sitter black hole metric featuring novel $r^{-6}$ and $r^{-14}$ correction terms. The horizon structure can exhibit up to four horizons depending on the parameters. Thermodynamic analysis reveals that the heat capacity exhibits critical phase transitions, with the critical point significantly shifted by the coupled corrections. Using the effective metric formalism, we study the photon sphere and black hole shadow, finding that the magnetic charge $Q$ shrinks the shadow while the nonlinear parameter $γ$ enlarges it. Constraints from Event Horizon Telescope observations of M87* and Sgr A* place the parameter $γ$ at the order of $10^3$ at $1σ$ and $2σ$ confidence levels. Our results demonstrate that quadratic $f(R,T)$ gravity combined with nonlinear electrodynamics provides a consistent framework for strong-field gravity phenomenology.