Dynamical instability and expansion-free condition in $$f(R, T)$$ f ( R , T ) gravity

A dynamical analysis of a spherically symmetric collapsing star surrounded by a locally anisotropic environment under an expansion-free condition is presented in $$f(R,T)$$ gravity, where $$R$$ corresponds to the Ricci scalar and $$T$$ stands for the trace of the energy momentum tensor. The modified field equations and evolution equations are reconstructed in the framework of $$f(R,T)$$ gravity. In order to acquire the collapse equation we implement the perturbation on all matter variables and dark source components comprising the viable $$f(R,T)$$ 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.

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