Gravastars formation with back-reaction effects from extended general relativity

Using an extended theory of General Relativity that incorporates normalized relativistic velocities, where the boundary terms in the varied Einstein–Hilbert action are considered. Within this context, I investigate the dynamic evolution of a collapsing spherical system characterized by a metric with spatial curvature and variable time-scale, aiming to describe the process of Gravastar formation. To illustrate the system’s dynamics, I analyze a power-law collapsing scenario and derive the equation of state for both cases, with and without geometrical perturbations. In particular, I derive the equation of state, incorporating back-reaction effects related with the boundary terms of the varied Einstein–Hilbert action.