Minimal geometric deformation in a Reissner–Nordström background
Ángel Rincón (Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2950, Casilla 4059, Valparaiso, Chile); Luciano Gabbanelli (Deptartament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, Barcelona, 08028, Spain); Ernesto Contreras (School of Physical Sciences and Nanotechnology, Yachay Tech University, Urcuquí, 100119, Ecuador); Francisco Tello-Ortiz (Departamento de Física, Facultad de ciencias básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile)
This article is devoted to the study of new exact analytical solutions in the background of Reissner–Nordström 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.