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

Understand

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 $A(r)$.