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.

在目前的工作中，我们研究了通过最小几何变形方法通过重力解耦来获得描述拉斯塔尔重力框架内各向异性物质分布的静态自重系统恒星内部的可能性。由于拉索尔引力破坏了最小耦合物质原理，因此我们对这种情况下的以色列—达莫瓦伊交界条件是如何工作进行了详尽的解释。此外，为了获得变形的时空，已经使用了模拟约束程序。为了检查该建议的可行性，我们已将其应用于众所周知的Tolman IV解决方案。给出了由其他来源引入的效应的完整热力学描述。另外，在纯广义相对论，纯Rastall重力图中以及在广义相对论包括引力解耦的框架中，将结果与它们的比喻进行了比较。为了进行数学和图形分析，我们采用了重力解耦常数$\alpha$ 和Rastall的参数 $\lambda$作为自由参数，描述广义相对论扇区的紧密度系数为0.2。此外，为了提供更真实的图片，我们对两个参数进行了限制$\alpha$ 和 $\lambda$通过使用真实的观测数据来探索该特定模型下该理论的局限性。通过使用这种方法，建议用于研究中子或夸克星的应用。