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We continue the study of ``dynamical gravastars'', constructed by solving theTolman-Oppenheimer-Volkoff (TOV) equation with relativistic matter, undergoinga phase transition at high pressure to a state with negative energy density, asallowed in quantum theory. Since generation of a horizon-like structure or``simulated horizon'' occurs at a radius above where the phase transitionoccurs, it is solely a property of the TOV equation with relativistic matter,for appropriate small radius initial conditions. We survey the formation of asimulated horizon from this point of view. From the numerical solutions, weshow that the metric exponent appearing in the TOV equation undergoes an arctangent-like jump, leading to formation of the simulated horizon. Rescaling theproblem to fixed initial radius, we plot the ``phase diagram'' in the initialpressure--initial mass plane, showing the range of parameters where a simulatedhorizon dynamically forms.

Dynamical Gravastar "Simulated Horizon'' from TOV Equation Initial Value Problem with Relativistic Matter