This paper aims to determine the anisotropic solutions for static spherically symmetric spacetime via gravitational decoupling technique in the context of $f(G,T)$ gravity, where $G$ indicates the Gauss–Bonnet term and $T$ represents trace of the energy-momentum tensor. The additional source, present alongside the isotropic seed source in the sphere, induces anisotropy in the system. In order to decouple the two sources, we impose a minimal geometric deformation on the radial metric component which gives rise to two sets. The first array represents the isotropic system while the second set corresponds to the anisotropic structure. In order to determine the solution of first set, we use the metric potentials of the Tolman V spacetime while two solutions of the second set are extracted with the help of two constraints on the components of the additional source. These solutions are combined with the solution of the first set to formulate two extensions of Tolman V spacetime. The matching between the interior and exterior geometries yields the values of unknown constants. Furthermore, the viability and stability of the obtained solutions are checked for different values of the parameters. It is concluded that both solutions are viable and the first solution is stable as well, while the second solution shows unstable behavior.

本文旨在通过引力解耦技术确定静态球对称时空的各向异性解。$F(G,吨)$重力，在哪里$G$表示 Gauss-Bonnet 项和$吨$表示能量-动量张量的轨迹。与球体中的各向同性种子源一起存在的附加源在系统中引起各向异性。为了解耦这两个源，我们对产生两个集合的径向度量分量施加最小几何变形。第一个数组表示各向同性系统，而第二组对应于各向异性结构。为了确定第一组的解，我们使用 Tolman V 时空的度量势，而第二组的两个解是在附加源分量的两个约束的帮助下提取的。这些解与第一组的解相结合，形成了 Tolman V 时空的两个扩展。内部和外部几何形状之间的匹配产生未知常数的值。此外，针对不同的参数值检查所获得解决方案的可行性和稳定性。结论是两种解决方案都是可行的，第一个解决方案也很稳定，而第二个解决方案表现出不稳定的行为。