In this paper, we have explored the non-static anisotropic gravitational collapse and expansion solutions in Rastall theory of gravity. The field equations have been formulated for the non-static and inhomogeneous gravitating source. The Misner–Sharp mass function, auxiliary solution and trapped condition have been used to obtained a trapped surface. The auxiliary solutions have been used to obtain the expansion and collapse solutions; these solutions depend on [Formula: see text] and parameter [Formula: see text] (which appears due to parametric form of metric components); also the range of parameter [Formula: see text] has been examined. The expansion scalar [Formula: see text] depends on parameter [Formula: see text], in the case of expansion [Formula: see text] for [Formula: see text], while for collapse [Formula: see text] with [Formula: see text]. Also, the dynamics of the gravitating spherical source has been discussed graphically with the effects of Rastall parameter [Formula: see text]. For the physically reasonable fluid, the validity of energy conditions has been discussed for expansion and collapse solutions with the various values of [Formula: see text].

中文翻译：

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Rastall 引力中的非静态和非均匀引力源模型

在本文中，我们探讨了 Rastall 引力理论中的非静态各向异性引力坍缩和膨胀解。已经为非静态和非均匀引力源制定了场方程。Misner-Sharp 质量函数、辅助解和捕获条件已用于获得捕获表面。辅助解已用于获得膨胀解和塌缩解；这些解决方案取决于 [公式：参见文本] 和参数 [公式：参见文本]（由于度量组件的参数形式而出现）；还检查了参数 [公式：见正文] 的范围。展开标量[公式：见文本]取决于参数[公式：见文本]，在展开[公式：见文本]的情况下为[公式：见文本]，而对于折叠[公式：见文本]与[公式：见正文]。此外，还以图形方式讨论了引力球面源的动力学以及 Rastall 参数的影响 [公式：见正文]。对于物理上合理的流体，能量条件的有效性已经讨论了膨胀和坍塌解的各种值[公式：见正文]。