<p>This study explores the dynamical instability of axially symmetric, anisotropic stellar structures within the framework of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ f(R, T) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> gravity, utilizing a radial perturbation approach and an equation of state linking static and dynamic variables via the adiabatic index. The analysis examines deviations in geometric and material configurations during gravitational collapse. The chosen modified gravity model incorporates both the Ricci scalar <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ R $</EquationSource> <EquationSource Format="MATHML"><math> <mi>R</mi> </math></EquationSource> </InlineEquation> and the trace of the energy-momentum tensor <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ T $</EquationSource> <EquationSource Format="MATHML"><math> <mi>T</mi> </math></EquationSource> </InlineEquation> in the Lagrangian. Stability criteria are derived under Newtonian and post-Newtonian approximations, emphasizing the critical role of the adiabatic index in identifying instability regimes. The study specifically addresses inequalities for the adiabatic index within minimally coupled logarithmic <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ f(R, T) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> models. At the same time, results highlight that hydrostatic equilibrium relies on a delicate balance among gravitational, anti-gravitational, and effective pressure forces. Any deviation from this balance induces instability, further exacerbated by the influence of dark source terms inherent to the modified gravity framework.</p>

Identifying unstable regions in collapsing stars using radial perturbation techniques and relativistic corrections

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发表日期：

2025年9月25日

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M. Yousaf,
A. Rehman,
Sardor Sabirov

摘要

This study explores the dynamical instability of axially symmetric, anisotropic stellar structures within the framework of $ f(R, T) $ $f (R, T)$ gravity, utilizing a radial perturbation approach and an equation of state linking static and dynamic variables via the adiabatic index. The analysis examines deviations in geometric and material configurations during gravitational collapse. The chosen modified gravity model incorporates both the Ricci scalar $ R $ $R$ and the trace of the energy-momentum tensor $ T $ $T$ in the Lagrangian. Stability criteria are derived under Newtonian and post-Newtonian approximations, emphasizing the critical role of the adiabatic index in identifying instability regimes. The study specifically addresses inequalities for the adiabatic index within minimally coupled logarithmic $ f(R, T) $ $f (R, T)$ models. At the same time, results highlight that hydrostatic equilibrium relies on a delicate balance among gravitational, anti-gravitational, and effective pressure forces. Any deviation from this balance induces instability, further exacerbated by the influence of dark source terms inherent to the modified gravity framework.