Black holes and regular black holes in coincident $$f({\mathbb {Q}},{\mathbb {B}}_Q)$$ f ( Q , B Q ) gravity coupled to nonlinear electrodynamics

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