Novel charged black hole solutions in conformal Killing gravity

Abstract: In this paper, we investigate static spherically symmetric solutions in the context of Conformal Killing Gravity, a recently proposed modified theory of gravity that offers a new approach to the cosmological constant problem. Coupling this new theory with nonlinear electrodynamics, we derive the corresponding field equations and study their behavior under different parameter choices. We analyze three different models, each focusing on different key parameters. Our results reveal a rich causal structure with multiple horizons and transitions between extreme and non-extreme solutions depending on the parameter values. Moreover, we compute the nonlinear Lagrangian density for each model and find that it agrees with Maxwell theory in the limit $F \rightarrow 0$. We also confirm the existence of a central curvature singularity via the Kretschmann scalar. To connect our theoretical results with observational prospects, we study the black hole shadows associated with each model. The analysis shows that the calculated shadow size and shape of the three proposed models are consistent with the data for the supermassive object at the center of our galaxy and are therefore possible candidates for modeling this structure.