Unstable Regions of Anisotropic Relativistic Spheres in Higher-Dimensions

Abstract

Abstract In this work, we consider the collapse of a $\mathbb{D}$-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 $\mathbb{D}$-dimensional modified term.
This work investigates the criteria for dynamical instability of
anisotropic relativistic sphere systems with
$\mathbb{D}$-dimensional modified gravity. The certain conditions are
applied that lead to the collapse equation and their effects on
adiabatic index $\Gamma$ in both Newtonian (N) and Post-Newtonian
(PN) regimes by using a perturbation scheme. The study explores that
the $\Gamma$ plays a crucial role in determining the degree of
dynamical instability. This index characterizes the fluid's
stiffness and has a significant i7mpact on defining the ranges of
instability. This systematic investigation demonstrates the
influence of various material properties such as anisotropic
pressure, kinematic quantities, mass function, $\mathbb{D}$-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.