The present paper is devoted to investigating the possibility of getting stellar interiors for ultra-dense compact spherical systems portraying an anisotropic matter distribution, employing the gravitational decoupling by means of Minimal Geometric Deformation (MGD) procedure within the modified theory of gravity: $f(R,T)$. In this regard, we have considered the algebraic function as $f(R,T)=R+2\chi T$. The corresponding effective stress–energy tensor is conserved as well as the exact solutions are derived, where $\chi$ indicates a coupling constant which incorporates a new gravity aspect in the system. However, the MGD was introduced through a coupling constant $\alpha$ which makes the fluid go beyond to the perfect fluid–structure (i.e. introduce anisotropy). In this connection, we also discussed how both parameters $\alpha$ and $\chi$ affect the system. Moreover, the physical quantities associated with the new solutions are well-behaved from the physical and mathematical point of view which are affirmed by performing several physical tests of the main salient features, such pressure, density, dynamical equilibrium, energy conditions, and dynamical stability. We also performed the junction conditions for this chosen linear $f(R,T)$ function. On the other hand, we have generated the $M-R$ curves from our solutions in different scenarios, including GR, GR+MGD, $f(R,T)$ and $f(R,T)+$MGD, and we found a perfect fit for many compact spherical objects in these scenarios by varying $\alpha$ and $\chi$. The present study reveals that the modified $f(R,T)$ gravity through gravitational decoupling by means of MGD method is a suitable theory to explain compact stellar structures.

本文致力于研究在描述重力理论的基础上采用最小几何变形（MGD）方法进行重力解耦的方法来描绘具有各向异性物质分布的超致密球形系统的恒星内部： $F（\mathrm{[R}，Ť）$。在这方面，我们认为代数函数为$F（\mathrm{[R}，Ť）=\mathrm{[R}+2\chi Ť$。保留了相应的有效应力-能量张量，并推导了精确解，其中$\chi$表示耦合常数，在系统中结合了新的重力方面。但是，MGD是通过耦合常数引入的$\alpha$这使流体超出了理想的流体结构（即引入了各向异性）。在这方面，我们还讨论了两个参数$\alpha$ 和 $\chi$影响系统。此外，从物理和数学的角度来看，与新解决方案关联的物理量表现良好，可以通过对主要显着特征（例如压力，密度，动态平衡，能量条件和动态稳定性）进行几次物理测试来确认。我们还为所选的线性模型执行了结条件$F（\mathrm{[R}，Ť）$功能。另一方面，我们生成了$\mathrm{中号}-\mathrm{[R}$ 我们的解决方案在不同情况下的曲线，包括GR，GR + MGD， $F（\mathrm{[R}，Ť）$ 和 $F（\mathrm{[R}，Ť）+$MGD，我们发现，通过改变 $\alpha$ 和 $\chi$。本研究表明，修改后的$F（\mathrm{[R}，Ť）$ MGD方法通过重力解耦产生的重力是解释致密恒星结构的合适理论。