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

A. Zahra, S. A. Mardan, Muhammad Bilal Riaz, Javlon Rayimbaev, Inomjon Ibragimov, Munisbek Akhmedov, Erkaboy Davletov

TL;DR

This work addresses the nonlinear evolution of anisotropic self-gravitating configurations in $f(R)$ gravity with higher-order curvature corrections, adopting the Starobinsky model $f(R)=R+αR^2$ and the generalized Tolman–Kuchowicz metric to model a DM-influenced compact star. The authors derive modified field equations, implement the GTK metric with a parameter $n$, and apply the model to the neutron star candidate Her X-1, ensuring regularity and physical viability via energy conditions, TOV balance, causality, and the adiabatic index. They reveal that increasing the GTK parameter $n$ amplifies the DM-like curvature effects, raising central density and pressures, widening anisotropy, and strengthening internal forces while preserving singularity-free configurations; the resulting mass–radius behavior aligns with observational constraints. The study demonstrates that DM effects can be encoded geometrically within $f(R)$ gravity and examined through precise stellar structure diagnostics, offering a framework to test higher-order curvature corrections against compact-object observables and motivating extensions to other modified gravity theories.

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 $f(R) = R + αR^2$, 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.

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

TL;DR

This work addresses the nonlinear evolution of anisotropic self-gravitating configurations in gravity with higher-order curvature corrections, adopting the Starobinsky model and the generalized Tolman–Kuchowicz metric to model a DM-influenced compact star. The authors derive modified field equations, implement the GTK metric with a parameter , and apply the model to the neutron star candidate Her X-1, ensuring regularity and physical viability via energy conditions, TOV balance, causality, and the adiabatic index. They reveal that increasing the GTK parameter amplifies the DM-like curvature effects, raising central density and pressures, widening anisotropy, and strengthening internal forces while preserving singularity-free configurations; the resulting mass–radius behavior aligns with observational constraints. The study demonstrates that DM effects can be encoded geometrically within gravity and examined through precise stellar structure diagnostics, offering a framework to test higher-order curvature corrections against compact-object observables and motivating extensions to other modified gravity theories.

Abstract

This study examines the dynamical evolution of self-gravitating systems in the presence of exotic matter within the framework of gravity. Specifically, we have adopted the Starobinsky model , 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 described by the generalized Tolman-Kuchowicz metric, demonstrating a singularity-free behavior of the physical parameters. The results reveal that increasing the parameter 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.

Paper Structure

This paper contains 12 sections, 27 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Derivation of modified field equations in $f(R)$ gravity
  3. Stellar configurations in $f(R)$ gravity with the GTK metric and the Starobinsky model
  4. Physical viability of matter components in $f(R)$ gravity
  5. Regularity conditions in $f(R)$ gravity theory
  6. The exterior spacetime and boundary conditions
  7. Physical analysis of Starobinsky model with generalized Tolman--Kuchowicz metric
  8. Energy conditions
  9. The hydrostatic equilibrium condition
  10. Adiabatic index
  11. Causality conditions and Herrera cracking technique
  12. Conclusion and Discussion

Figures (14)

  • Figure 1: Graph of $\rho^{eff}~(km^{-2})$ with respect to radial variation $r~(km)$ for $Her~ X-1$ through various GTK parametric values $n=1,~1.5,~2,~2.5$.
  • Figure 2: Graph of $p_r^{eff}~(km^{-2})$ with respect to radial variation $r~(km)$ for $Her~ X-1$ through various GTK parametric values $n=1,~1.5,~2,~2.5$.
  • Figure 3: Graph of $p_t^{eff}~(km^{-2})$ with respect to radial variation $r~(km)$ for $Her~ X-1$ through various GTK parametric values $n=1,~1.5,~2,~2.5$.
  • Figure 4: Graph of $\Delta~(km^{-2})$ with respect to radial variation $r~(km)$ for $Her~ X-1$ through various GTK parametric values $n=1,~1.5,~2,~2.5$.
  • Figure 5: Graph of $\frac{d\rho^{eff}}{dr}~(km^{-3})$ with respect to radial variation $r~(km)$ for $Her~ X-1$ through various GTK metric values $n=1,~1.5,~2,~ric5$.
  • ...and 9 more figures