The aim of this paper is to present the definition of complexity for static self-gravitating anisotropic matter proposed in $f(G,T)$ theory, where $G$ is the Gauss-Bonnet term and $T$ is the trace of energy momentum tensor. We evaluate field equations, Tolman-Oppenheimer-Volkoff equation, mass functions and structure scalars. Among the calculated modified scalar variables that are obtained from the orthogonal splitting of Riemann tensor, a single scalar function has been identified as the complexity factor. After exploring the corresponding Tolmann mass function, it is seen that the complexity factor along with the $f(G,T)$ terms have greatly influenced its formulation and its role in the subsequent radial phases of the spherical system. We have also used couple of ansatz in order to discuss possible solutions of equations of motion in the study of the structure of compact object.

中文翻译：

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使用结构标量测量自引力系统的复杂性

本文的目的是提出 $f(G,T)$ 理论中提出的静态自引力各向异性物质的复杂性定义，其中 $G$ 是 Gauss-Bonnet 项，$T$ 是能量轨迹动量张量。我们评估场方程、Tolman-Oppenheimer-Volkoff 方程、质量函数和结构标量。在由黎曼张量正交分裂得到的计算修正标量变量中，单个标量函数被确定为复杂度因子。在探索了相应的托尔曼质量函数后，可以看出复杂性因子与 $f(G,T)$ 项一起极大地影响了它的公式及其在球形系统的后续径向阶段中的作用。