Axially Symmetric Shear-free Fluids in $f(R,T)$ Gravity

TL;DR

This paper investigates the stability of shear-free, axially symmetric anisotropic fluids in $f(R,T)$ gravity, deriving conditions for stability and instability in Newtonian and post-Newtonian regimes.

Contribution

It introduces a detailed analysis of shear-free axially symmetric fluids in $f(R,T)$ gravity, deriving evolution equations and stability criteria considering dark sources.

Findings

Derived instability range for axially symmetric fluids

Established relation between adiabatic index and stability

Analyzed stability in Newtonian and post-Newtonian limits

Abstract

In this work we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection enteries is taken into account for establishment of instability range. Implementation of linear perturbation on constitutive modified dynamical equations yield evolution equation. This equation associates adiabatic index $\Gamma$ with material and dark source components defining stable and unstable regions in Newtonian (N) and post-Newtonian (pN) approximations.