Black bounce solutions via nonminimal scalar-electrodynamic couplings

Abstract: Black-bounce (BB) solutions generalize the spacetimes of black holes, regular black holes, and wormholes, depending on the values of certain characteristic parameters. In this work, we investigate such solutions within the framework of General Relativity (GR), assuming spherical symmetry and static geometry. It is well established in the literature that, in order to sustain such geometries, the source of Einstein's equations in the BB context can be composed of a scalar field $\varphi$ and a nonlinear electrodynamics (NLED). In our model, in addition to the Lagrangian associated with the scalar field in the action, we also include an interaction term of the form $W(\varphi)\mathcal{L}(F)$, which introduces a nonminimal coupling between the scalar field and the electromagnetic sector. Notably, the usual minimal coupling configuration is recovered by setting $W(\varphi)=1$. In contrast to approaches where the function $W(\varphi)$ is assumed a priori, here we determine its functional form by modeling the radial dependence of the derivative of the electromagnetic Lagrangian as a power law, namely $\mathcal{L}_F(r) \sim F^n$. This approach enables us to determine $W(r)$ directly from the obtained solutions. We apply this procedure to two specific geometries: the Simpson-Visser-type BB solution and the Bardeen-type BB solution, both analyzed in the purely magnetic ($q_m \neq 0$, $q_e=0$) and purely electric ($q_m=0$, $q_e \neq 0$) cases. In all scenarios, we find that these BB spacetime solutions can be described with a linear electrodynamics, which is a noteworthy result. Furthermore, we examine the regularity of the spacetime through the Kretschmann scalar and briefly discuss the associated energy conditions for the solutions obtained.