A novel definition of complexity in torsion based theory

Despite coming across quite effective definitions of complexity in terms of many modified theories of gravity, it still has a question about its existence in f(T) gravity, where the torsion scalar T is accountable for gravitational impacts. The emergence of complexity factor is due to division of intrinsic curvature in an orthogonal way as described by Herrera (Phys Rev D 97:044010, 2018). To initiate the analysis, we reckon the interior region is like a spherically symmetric static configuration filled by the locally anisotropic fluid and exteriorly associated with a spherical hypersurface. In this framework, we acquire the f(T) field equations and utilize the already formulated relationship between the intrinsic curvature and the conformal tensor to perform our analysis. We bring into action the definitions of the two frequently availed masses (Tolman and Misner–Sharp) for spherical composition and investigate the appealing correlation between them and the conformal tensor. The impact of the local anisotropy and the homogeneity and inhomogeneity of energy density has substantial importance in this regard. We build up some relation in terms of already defined variables and interpret the complexity as a single scalar YTF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_{TF}$$\end{document}. It deduce that this factor vanished when the fluid content is homogenous and also when the impact of two anisotropic terms cancel out in the case of inhomogeneous fluid content. We determine a few definite interior solutions which fulfill the criterion of vanishing scalar YTF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_{TF}$$\end{document}. Certain defined ideas in fulfillment of the vanishing complexity factor constraint, are applied for f(T) gravity.