I give new results for  “gravastars'', which are horizonless compact objects that closely mimic mathematical black holes in their exterior geometry,  but for which g_{00} is always positive.  They result from  solving the  Tolman-Oppenheimer-Volkoff  (TOV) equations for relativistic stellar structure, which require continuous pressure, but with an interior density jump from a normal matter equation of state, to an equation of state where pressure plus density  approximately sum to zero. 
We present Mathematica notebooks solving the TOV equations, in which the structure of the gravastar is entirely governed by the Einstein-Hilbert gravitational action (with zero cosmological constant) together with  the matter equation of state, with  radii where structural changes occur  emerging from the dynamics, rather than being specified in advance.   To conclude, I'll extend the model to include a cosmological constant, and discuss possible astrophysical implications of absence of a horizon.