In this work, we consider an extension of the symmetric teleparallel equivalent of General Relativity (STEGR), namely, $f(\mathbb{ Q})$ gravity, by including a boundary term $\mathbb{ B}_Q$, where $\mathbb{ Q}$ is the non-metricity scalar. More specifically, we explore static and spherically symmetric black hole and regular black hole solutions in $f(\mathbb{ Q},\mathbb{ B}_Q)$ 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 $f_Q = -f_B$, where $f_{ Q}=\partial f/\partial\mathbb{ Q}$ and $f_{ B}= \partial f/\partial\mathbb{ B}_Q$. 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 ${ \cal L}_{ \rm NLED}(F)$. Furthermore, we also obtain generalized solutions of the Bardeen and Culetu types of regular black holes, by imposing specific metric functions.
Categories: gr-qc hep-th