On the Stability of Pressure Isotropy Condition in Palatini $f(R)$ Gravity

TL;DR

This paper investigates the stability of pressure isotropy in spherically symmetric dissipative systems within Palatini $f(R)$ gravity, deriving differential equations involving the Weyl scalar and analyzing anisotropic evolution.

Contribution

It introduces a differential equation based on the Weyl scalar to analyze pressure isotropy stability in Palatini $f(R)$ gravity, extending to axially symmetric configurations.

Findings

Derived a key differential equation involving the Weyl scalar.

Identified physical factors like energy density, dissipative flux, and shear as triggers for anisotropy.

Extended analysis from spherical to axially symmetric configurations.

Abstract

This manuscript copes with the issue of analyzing the conditions to check the stability of the pressure isotropy condition by taking into account a spherically symmetric dissipative astrophysical configuration with the Palatini $f(R)$ gravity theory. We work out a differential equation in terms of the Weyl scalar that has a crucial part in the analysis of the evolution of the considered system. Using this equation, we devise another stellar equation that characterizes the evolution of anisotropic factor. Later, we assume an axially symmetric configuration and extended our analysis for that particular symmetry. It is worth observing that the physical factors responsible for compelling an initially isotropic object to trigger pressure anisotropy incorporate energy density, dissipative flux, and shear in fluid flow.