Complexity analysis of Cylindrically Symmetric Self-gravitating Dynamical System in $f(R,T)$ Theory of Gravity

TL;DR

This paper investigates the complexity of cylindrically symmetric self-gravitating systems within $f(R,T)$ gravity, analyzing how higher-order curvature terms influence system complexity and stability during evolution.

Contribution

It introduces a novel analysis of complexity factors in $f(R,T)$ gravity for cylindrical systems, considering multiple models and evolutionary conditions.

Findings

Complexity increases with higher-order curvature terms.

Higher order trace terms influence complexity but are less crucial in minimal coupling.

Stability of zero complexity condition is discussed.

Abstract

In this article, we have studied a cylindrically symmetric self-gravitating dynamical object via complexity factor which is obtained through orthogonal splitting of Reimann tensor in $f(R,T)$ theory of gravity. Our study is based on the definition of complexity for dynamical sources, proposed by Herrera \cite{12b}. We actually want to analyze the behavior of complexity factor for cylindrically symmetric dynamical source in modified theory. For this, we define the scalar functions through orthogonal splitting of Reimann tensor in $f(R,T)$ gravity and work out structure scalars for cylindrical geometry. We evaluated the complexity of the structure and also analyzed the complexity of the evolutionary patterns of the system under consideration. In order to present simplest mode of evolution, we explored homologous condition and homogeneous expansion condition in $f(R,T)$ gravity and discussed dynamics and kinematics in the background of a generic viable non-minimally coupled $f(R,T)=\alpha_1 R^m T^n +\alpha_2 T(1+\alpha_3 T^p R^q)$ model. In order to make a comprehensive analysis, we considered three different cases (representing both minimal and non-minimal coupling) of the model under consideration and found that complexity of a system is increased in the presence of higher order curvature terms, even in the simplest modes of evolution. However, higher order trace terms affects the complexity of the system but they are not crucial for simplest modes of evolution in the case of minimal coupling. The stability of vanishing of complexity factor has also been discussed.