Minimal Geometric Deformation in a Reissner-Nordstr\"om background

This article is devoted to the study of new exact analytical solutions in the background of Reissner-Nordstr\"{o}m space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general equation of state, relating the components of the $\theta$-sector in order to obtain the new material contributions and the decoupler function $f(r)$. Besides, we obtain the bounds on the free parameters of the extended solution to avoid new singularities. Furthermore, we show the finitude of all thermodynamic parameters of the solution such as the effective density $\tilde{\rho}$, radial $\tilde{p}_{r}$ and tangential $\tilde{p}_{t}$ pressure for different values of parameter $\alpha$ and the total electric charge $Q$. Finally, the behavior of some scalar invariants, namely the Ricci $R$ and Kretshmann $R_{\mu\nu\omega\epsilon}R^{\mu\nu\omega\epsilon}$ scalars are analyzed. It is also remarkable that, after an appropriate limit, the deformed Schwarzschild black hole solution always can be recovered.