The present article is devoted to the study of local anisotropies effects on the Durgapal's fourth model in the context of gravitational decoupling via the Minimal Geometric Deformation approach. To do it, the most general equation of state relating the components of the $\theta$--sector is imposed to obtain the decoupler function $f(r)$. In addition, certain properties of the obtained solution are investigated, such as the behavior of the salient material content threading the stellar interior, causality and energy conditions, hydrostatic balance through modified Tolman--Oppenheimer--Volkoff conservation equation and stability mechanism against local anisotropies by means of adiabatic index, sound velocity of the pressure waves, convection factor and Harrison--Zeldovich--Novikov procedure, in order to check if the model is physically admissible or not. Regarding the stability analysis, it is found that the model presents unstable regions when the sound speed of the pressure waves and convection factor are used in distinction with what happens in the adiabatic index and Harrison--Zeldovich--Novikov case. To produce a more realistic picture the numerical data for some known compact objects was placed and different values of the parameter $\alpha$ were considered to compare with the GR case i.e, $\alpha=0$.

中文翻译：

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基于最小几何变形方法的 Durgapal IV 模型

本文致力于通过最小几何变形方法在引力解耦的背景下研究局部各向异性对 Durgapal 第四模型的影响。为此，将与 $\theta$--扇区的组件相关的最一般状态方程强加于获得解耦函数 $f(r)$。此外，还研究了所得解的某些性质，例如穿过恒星内部的显着物质含量的行为、因果关系和能量条件、通过改进的 Tolman--Oppenheimer--Volkoff 守恒方程的流体静力平衡以及针对局部各向异性的稳定性机制通过绝热指数、压力波的声速、对流因子和Harrison--Zeldovich--Novikov过程，为了检查模型是否物理上可接受。关于稳定性分析，发现当压力波的声速和对流因子被用于区分绝热指数和Harrison--Zeldovich--Novikov情况时，模型呈现不稳定区域。为了产生更逼真的图片，放置了一些已知紧凑物体的数值数据，并考虑将参数 $\alpha$ 的不同值与 GR 情况进行比较，即 $\alpha=0$。