Abstract
This paper is devoted to study the stability/instability of the expansionfree self gravitating source in the framework of Einstein Gauss-Bonnet gravity. The source has been taken as Tolman-Bondi model which is homogenous in nature. The field equations as dynamical equations have been evaluated in Gauss-Bonnet gravity in five dimensions. The junction conditions as well as cavity evaluations equations have been explored in detail. The perturbation scheme of first order has been applied to dynamical as Einstein Gauss-Bonnet field equations. The concept of Newtonian as well post Newtonian approximation have been used to derive general dynamical stability equations. In general this equation represents the stability of the gravitating source. Some particular values of system parameters have been chosen to prove the concept of stability graphically. It has been mentioned that other than choosing the particular values of the parameters the stability of the system will be disturbed, hence it would leads to instability.
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