https://doi.org/10.1140/epjc/s10052-015-3289-9
Regular Article - Theoretical Physics
Dynamical instability and expansion-free condition in 
gravity
1
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2
Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan
* e-mail: mzubairkk@gmail.com
** e-mail: drmzubair@ciitlahore.edu.pk
Received:
26
November
2014
Accepted:
21
January
2015
Published online:
10
February
2015
A dynamical analysis of a spherically symmetric collapsing star surrounded by a locally anisotropic environment under an expansion-free condition is presented in 
gravity, where 
corresponds to the Ricci scalar and 
stands for the trace of the energy momentum tensor. The modified field equations and evolution equations are reconstructed in the framework of gravity. In order to acquire the collapse equation we implement the perturbation on all matter variables and dark source components comprising the viable model. The instability range is described in the Newtonian and post-Newtonian approximation. It is observed that the unequal stresses and density profile define the instability range rather than the adiabatic index. However, the physical quantities are constrained to maintain positivity of the energy density and a stable stellar configuration.
© SIF and Springer-Verlag Berlin Heidelberg, 2015
