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 2-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.