Abstract

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. In my initial formulation, 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 as in the original Mazur-Mottola gravastars.

My more recent work with a student shows that the interesting ``simulated horizon’’ structure of dynamical gravastars is a property solely of the exterior TOV equations for relativistic matter with appropriate small radius boundary conditions, and will be present for a large class of interior equations of state. The exterior TOV equations can be rewritten in rescaling-invariant form, leading to a two dimensional autonomous system of differential equations which are now being studied numerically and analytically , and for which hopefully some rigorous results can be proved.