  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.

General Physics