Definition of Complexity Factor for Self-Gravitating Systems in Palatini $f(R)$ Gravity

TL;DR

This paper defines and analyzes a complexity factor for static, self-gravitating spheres in Palatini $f(R)$ gravity, exploring how matter variables and modified gravity influence their structure and evolution.

Contribution

It adapts the complexity factor concept to static spheres within Palatini $f(R)$ gravity, providing analytical models and insights into matter and gravity effects on structure formation.

Findings

Complexity factor depends on matter anisotropy and $f(R)$ modifications.

Analytical models illustrate the influence of gravity and matter variables.

The approach links structure scalars to the evolution of self-gravitating systems.

Abstract

The aim of this paper is to explore the complexity factor (CF) for those self-gravitating relativistic spheres whose evolution proceeds non-dynamically. We are adopting the definition of CF mentioned in \cite{PhysRevD.97.044010}, modifying it to the static spherically symmetric case, within the framework of a modified gravity theory (the Palatini $f(R)$ theory). In this respect, we have considered radial dependent anisotropic matter content coupled with spherical geometry and determined the complexity factor involved in the patterns of radial evolution. We shall explore the field and a well-known Tolman-Oppenheimer-Volkoff equations. After introducing structure scalars from the orthogonal decomposition of the Riemann tensor, we shall calculate complexity factor. An exact analytical model is presented by considering firstly ansatz provided by Gokhroo and Mehra. The role of matter variables and $f(R)$ terms are analyzed in the structure formation as well as their evolution through a complexity factor.