Eur. Phys. J. A (2018) 54: 122
https://doi.org/10.1140/epja/i2018-12556-8

Regular Article - Theoretical Physics

Dynamical instability of spherical anisotropic sources in gravity

¹ Department of Mathematics, University of the Punjab, Quaid-i-Azam Campus, 54590, Lahore, Pakistan
² Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, 960-1296, Fukushima, Japan

^* e-mail: zeeshan.math@pu.edu.pk

Received: 15 March 2018
Accepted: 19 June 2018
Published online: 17 July 2018

Abstract

In this paper, we study the effects of modification of gravity on the problem of dynamical instability of the spherical relativistic anisotropic interiors. We have considered non-zero influence of expansion scalar throughout during the evolutionary phases of spherical geometry that led to the use of the fluid stiffness parameter. The modified hydrostatic equation for the stellar anisotropic matter distributions is constructed and then solved by using a radial perturbation scheme. Such a differential equation can be further used to obtain instability constraints at both weak field and post-Newtonian approximations after considering a particular Harrison-Wheeler equation of state. This approach allows us to deal with the effects of usual and effective matter variables on the stability exotic stellar of self-gravitating structures.