In this work, we investigated an inhomogeneous spherically symmetric star consisting of dust fluid and dark energy components. We obtained similarity solutions for the energy density of the inhomogeneous dust fluid \(\rho (t,r)\), dark energy \(\rho _{DE}(t,r)\), and the mass function inside the star m(t, r). The symmetries of Einstein field equations for this model are derived using the symmetry group analysis method, where the Einstein field equations have been reduced into nonlinear ordinary differential equations (NODEs). Some interesting explicit analytical solutions are obtained for the reduced NODEs. Consequently, a new class of similarity solutions has been obtained for the energy density of the inhomogeneous dust fluid and dark energy as functions of coordinates t and r. These solutions are obtained when the star is composed of both dust fluid and dark energy components, dark energy components only, and dust fluid only. When the star is composed of dust fluid only, we discussed the possibility of black hole formation by assuming that the collapsing star is not initially trapped. Graphical representations of some solutions are given and discussed in the last section.

在这项工作中，我们研究了一颗由尘埃流体和暗能量成分组成的非均匀球对称恒星。我们得到了非均匀尘埃流体 \（\rho （t，r）\）、暗能量 \（\rho _{DE}（t，r）\） 和恒星内部质量函数 m（t， r） 的能量密度的相似解。该模型的 Einstein 场方程的对称性是使用对称群分析方法推导的，其中 Einstein 场方程已简化为非线性常微分方程 （NODE）。对于约化的 NODEs，得到了一些有趣的显式解析解。因此，对于非均匀尘埃流体的能量密度和暗能量作为坐标 t 和 r 的函数，获得了一类新的相似性解。当恒星同时由尘埃流体和暗能量成分、仅暗能量成分和仅尘埃流体组成时，就会获得这些溶液。当恒星仅由尘埃流体组成时，我们通过假设坍缩的恒星最初没有被困住来讨论黑洞形成的可能性。上一节给出了一些解决方案的图形表示，并进行了讨论。