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

In this work, we consider an extension of the symmetric teleparallel equivalent of General Relativity (STEGR), namely, f(ℚ) gravity, by including a boundary term 𝔹_Q , where ℚ is the non-metricity scalar. More specifically, we explore static and spherically symmetric black hole and regular black hole solutions in 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 f_Q = -f_B , where f_Q=∂ f/∂ℚ and 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 ℒ_NLED(F) . Furthermore, we also obtain generalized solutions of the Bardeen and Culetu types of regular black holes, by imposing specific metric functions.