  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, as
allowed in quantum theory. Since generation of a horizon-like structure or
"simulated horizon" occurs at a radius above where the phase transition occurs,
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. From the numerical solutions, we
show that the metric exponent appearing in the TOV equation undergoes an arc
tangent-like jump, leading to formation of the simulated horizon. 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 consisting of a 2-dimensional autonomous
system of first order differential equations, for further analytical study.
