Charged anisotropic compact star in f(R,mathcal{T}) gravity: A minimal geometric deformation gravitational decoupling approach

This article is devoted to the study of high dense charged anisotropic compact structures in the framework of $f(R,\mathcal{T})$ gravity theory. The principal aims of this investigation, regard the extension of the isotropic Durgapal-Fuloria model within the context of charged isotropic $f(R,\mathcal{T})$ solutions. The second main goal of this work is to apply the gravitational decoupling via a minimal geometric deformation (MGD) scheme in $f(R,\mathcal{T})$ gravity. Finally, the third one is to derive an anisotropic version of the charged isotropic model previously obtained by applying gravitational decoupling technology. This MGD approach splits the system of equations into two separate sets, one corresponding with the f(R,$\mathcal{T}$) gravity system and another corresponding to the anisotropic sector governed by the extra source $\theta_{\mu\nu}$.To address this task we have considered some ingredients: I) the f(R,$\mathcal{T}$) model corresponds to a linear functional of the Ricci's scalar and the trace of the energy-momentum tensor $\mathcal{T}$, specifically $ f(R,\mathcal{T}) =R+2\chi\mathcal{T}$, being $\chi$ a running coupling constant. II) The matter distribution is taken to be an isotropic fluid one, III) the Lagrangian matter $\mathcal{L}_{m}$ corresponds to the negative isotropic pressure \i.e, $-p$ and IV) in order to solve the $\theta$-sector, a suitable form for the decoupler function $f(r)$ has been imposed, respecting all the physical and mathematical requirements. Finally, to check and contrast our model an exhaustive mathematical, physical and graphical analysis is performed in order to show all the properties that characterize the compact structure. It is worth mentioning that when $\chi=0$ Einstein's gravity theory results are recovered.