Black holes and regular black holes in coincident f(Q,BQ) gravity coupled to nonlinear electrodynamics

In this work, we consider an extension of the symmetric teleparallel equivalent of General Relativity (STEGR), namely, f(Q) f ( Q ) gravity, by including a boundary term BQ B Q , where Q Q is the non-metricity scalar. More specifically, we explore static and spherically symmetric black hole and regular black hole solutions in f(Q,BQ) f ( Q , B Q ) gravity coupled to nonlinear electrodynamics (NLED). In particular, to obtain black hole solutions, and in order to ensure that our solutions preserve Lorentz symmetry, we assume the following relation fQ = -fB f Q = - f B , where fQ=∂ f/∂ Q f Q = ∂ f / ∂ Q and fB= ∂ f/∂ BQ f B = ∂ f / ∂ B Q . We develop three models of black holes, and as the starting point for each case we consider the non-metricity scalar or the boundary term in such a way to obtain the metric functions A ( r ). Additionally, we are able to express matter through analytical solutions for specific NLED Lagrangians LNLED(F) L NLED ( F ) . Furthermore, we also obtain generalized solutions of the Bardeen and Culetu types of regular black holes, by imposing specific metric functions.