Unstable regions of anisotropic relativistic spheres in higher dimensions

Abstract In this work, we consider the collapse of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:math> -dimensional sphere in the framework of a higher-dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:math> -dimensional modified term. This work investigates the criteria for the dynamical instability of anisotropic relativistic sphere systems with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:math> -dimensional modified gravity. The certain conditions are applied that lead to the collapse equation and their effects on adiabatic index Γ in both Newtonian (N) and Post-Newtonian (PN) regimes by using a perturbation scheme. The study explores that the Γ plays a crucial role in determining the degree of dynamical instability. This index characterizes the fluid’s stiffness and has a significant impact on defining the ranges of instability. This systematic investigation demonstrates the influence of various material properties such as anisotropic pressure, kinematic quantities, mass function, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:math> -dimensional modified gravity parameters, and the radial profile of energy density on the instability of considered structures during their evolution. This work also displays the dynamical behavior of spherically symmetric fluid configuration via graphical approaches.