Nonlinear evolution of anisotropic matter configurations under higher-order curvature corrections

TL;DR

This paper investigates the nonlinear evolution of anisotropic matter in $f(R)$ gravity with higher-order curvature corrections, focusing on dark matter effects on compact objects like Her X-1, ensuring physical viability through various stability criteria.

Contribution

It introduces a detailed analysis of anisotropic matter evolution under $f(R)$ gravity with quadratic curvature corrections, emphasizing dark matter influence and stability of compact objects.

Findings

Dark matter significantly alters pressure distributions.

The model remains physically viable under multiple stability tests.

Variations in the metric parameter $n$ affect the internal structure.

Abstract

This study examines the dynamical evolution of self-gravitating systems in the presence of exotic matter within the framework of $f(R)$ gravity. Specifically, we have adopted the Starobinsky model $f(R) = R + \alpha R^2$, which incorporates higher-order curvature corrections to describe nonlinear gravitational behavior. The analysis focuses on the nonlinear spherical evolution of anisotropic matter configurations and explains how dark matter influences their physical characteristics. The presence of dark matter is found to significantly affect the radial and tangential pressure distributions, thereby altering the overall dynamics of the system. The model is employed for the compact object $ Her~X-1$ described by the generalized Tolman-Kuchowicz metric, demonstrating a singularity-free behavior of the physical parameters. The results reveal that increasing the parameter $n$ of the generalized Tolman-Kuchowicz metric leads to striking variations in the model characteristics, highlighting its essential role in governing internal structure and evolution of the compact object. The model remains physically viable under different testing criteria like energy conditions, hydrostatic equilibrium condition, adiabatic index, causality conditions, Herrera's Cracking condition and mass-radius relation presented in this work.