Decoupling gravitational sources by MGD approach in Rastall gravity

In the present work, we investigate the possibility of obtaining stellar interiors for static self-gravitating systems describing an anisotropic matter distribution in the framework of Rastall gravity through gravitational decoupling by means of minimal geometric deformation approach. Due to Rastall gravity breaks down the minimal coupling matter principle, we have provided an exhaustive explanation about how Israel-Darmois junction conditions work in this scenario. Furthermore, to obtain the deformed space-time, the mimic constraint procedure has been used. In order to check the viability of this proposal, we have applied it to the well known Tolman IV solution. A complete thermodynamic description of the effects introduced by the additional source is given. Additionally, the results have been compared with their similes in the picture of pure general relativity, pure Rastall gravity and within the framework of general relativity including gravitational decoupling. To perform the mathematical and graphical analysis we have taken the gravitational decoupling constant $\alpha$ and the Rastall's parameter $\lambda$ as free parameters and the compactness factor describing the general relativity sector to be $0.2$. Besides, to provide a more realistic picture we have bounded both parameters $\alpha$ and $\lambda$ by using real observational data to explore the limits of the theory under this particular model. Applications to study neutron or quark stars are suggested by using this methodology.