We presented a non-singular solution of Einstein’s field equations using gravitational decoupling by means of complete geometric deformation (CGD) in the anisotropic domain for compact star models. In this approach both the gravitational potentials are deformed as \( \nu =\xi +\beta \,h(r)\) and \( e^{-\lambda }=\mu +\beta \,f(r)\), where \(\beta \) is a coupling constant. Then we solve more complex field equations under above transformations by using a particular form of deformation function h(r) for two different cases namely the mimic constraint for the pressure \(\{p(r)=\theta ^1_1\}\) and the mimic constraint for the density \(\{\rho (r)=\theta _0^0\}\) (Ovalle in Phys Lett B 788:213, 2019). The compact star models have been constructed by taking \(M_0/R=0.2\) for two different non-zero values of \(\beta \). Moreover, the boundary conditions are also performed for the said complete geometric deformation in the presence of anisotropic matter distribution. We also find pressure, density, anisotropy and causality conditions that are physically acceptable throughout the model. The \(M-R\) curve is also presented to support our model for describing a realistic compact object such as neutron stars.

中文翻译：

---

完全几何变形（CGD）框架下重力解耦的各向异性模型非奇异解

对于紧凑星型模型，我们通过各向异性域中的完全几何变形（CGD），利用重力解耦提出了爱因斯坦场方程的非奇异解。在这种方法中，两个引力都变形为\（\ nu = \ xi + \ beta \，h（r）\）和\（e ^ {-\ lambda} = \ mu + \ beta \，f（r） \），其中\（\ beta \）是耦合常数。然后，针对两种不同的情况，即对压力\（\ {p（r）= \ theta ^ 1_1 \} \）的模拟约束，通过使用特定形式的变形函数h（r），我们可以求解上述变换下的更复杂的场方程。和密度\（\ {\ rho（r）= \ theta _0 ^ 0 \} \）的模拟约束（Phys Lett B 788：213中的椭圆，2019年）。通过对两个不同的非零值\（\ beta \）取\（M_0 / R = 0.2 \）来构造紧凑型星形模型。此外，在存在各向异性物质分布的情况下，还针对所述完全几何变形执行边界条件。我们还发现整个模型在物理上可接受的压力，密度，各向异性和因果条件。该\（MR \）曲线也呈现给支持我们的模型用于描述一个现实的致密天体，如中子星。