Gravastars formation with back-reaction effects from extended general relativity

Abstract

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.