Dynamical gravastar simulated horizon from the Tolman–Oppenheimer–Volkoff equation initial value problem with relativistic matter

We continue the study of “dynamical gravastars”, constructed by solving the Tolman–Oppenheimer–Volkoff (TOV) equations with relativistic matter, undergoing a phase transition at high pressure to a state with negative energy density. We define the “simulated horizon” as the horizon-like structure that appears, and which is a well-defined concept within the class of static, spherically symmetric metrics. Since the “simulated horizon” occurs at a radius above where the pressure-induced phase transition is postulated to occur, it is solely a property of the TOV equation with relativistic matter, for appropriate small radius initial conditions. We survey the formation of a simulated horizon from this point of view. Rescaling the problem to fixed initial radius, we plot the “phase diagram” in the initial pressure–initial mass plane, showing the range of parameters where a simulated horizon dynamically forms. Reformulating the TOV equations in rescaling-invariant form yields improved numerical results for the “phase diagram”, and gives a simplified model for further study consisting of a two-dimensional autonomous system of first-order differential equations. Our analysis gives a simple, natural answer to the question of how the radii where the phase transitions postulated in previous models of exotic compact objects are dynamically determined.