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

Abstract

In this work, we consider an extension of the symmetric teleparallel equivalent of General Relativity (STEGR), namely, $f(\mathbb{Q})$ 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 ${\mathcal{L}}_{\mathrm{NLED}}(F)$. Furthermore, we also obtain generalized solutions of the Bardeen and Culetu types of regular black holes, by imposing specific metric functions.

21 pages, 10 figures. V2: 25 pages, 15 figures; discussion and references added. Accepted for publication in EPJC

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