We develop multiple analytical solutions to the Rastall field equations using a recently proposed scheme, named the gravitational decoupling. In order to do this, we assume a spherical distribution that possesses anisotropic pressure in its interior and extend it by incorporating an additional gravitating source through the corresponding Lagrangian density. Such addition in the initial fluid distribution leads to the complicated field equations which are then tackled by implementing the minimal geometric deformation. This execution divides these equations into two different systems, each corresponds to the original source. The first system representing initial source is solved by adopting Krori–Barua and Tolman IV spacetimes, while three different constraints are used to work out the other set. The constants engaged in the above two ansatz are calculated through the junction conditions. The developed models are further explored graphically in the interior of a star, say 4U1820−30. Finally, we conclude our results to be physically feasible under the considered variation in both Rastall and decoupling parameters. It is important to mention here that the derived models can be viewed as idealized or toy models that serve as preliminary explorations within the framework of Rastall gravity.

中文翻译：

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各向同性和复杂性因子生成的 Krori-Barua 和 Tolman IV 模型上解耦和 Rastall 参数的作用


我们使用最近提出的一种称为引力解耦的方案，为 Rastall 场方程开发了多种解析解。为此，我们假设一个在其内部具有各向异性压力的球形分布，并通过相应的拉格朗日密度加入额外的引力源来扩展它。在初始流体分布中添加会导致复杂的场方程，然后通过实现最小的几何变形来解决这些方程。此执行将这些方程划分为两个不同的系统，每个方程对应于原始源。第一个表示初始源的系统是通过采用 Krori-Barua 和 Tolman IV 时空来解决的，而使用三种不同的约束来计算另一组。上述两个拟设中参与的常数是通过结条件计算的。在恒星内部以图形方式进一步探索开发的模型，例如 4U1820−30。最后，我们得出结论，在 Rastall 和 de耦参数的考虑变化下，我们的结果在物理上是可行的。这里需要提到的是，衍生的模型可以被视为理想化或玩具模型，作为 Rastall 引力框架内的初步探索。