Gravastars must have anisotropic pressures

TL;DR

This paper demonstrates that gravastars, as alternatives to black holes, must have anisotropic pressures in their structure, which allows for higher compactness and avoids the formation of horizons.

Contribution

It shows that perfect fluid models cannot support gravastars, establishing the necessity of anisotropic pressures and deriving bounds on pressure anisotropy using the TOV equation.

Findings

Gravastars require anisotropic pressures in their crust.

Anisotropic stresses allow higher compactness than perfect fluid stars.

The equation of state must support preventing horizon formation.

Abstract

One of the very small number of serious alternatives to the usual concept of an astrophysical black hole is the "gravastar" model developed by Mazur and Mottola; and a related phase-transition model due to Laughlin et al. We consider a generalized class of similar models that exhibit continuous pressure -- without the presence of infinitesimally thin shells. By considering the usual TOV equation for static solutions with negative central pressure, we find that gravastars cannot be perfect fluids -- anisotropic pressures in the "crust" of a gravastar-like object are unavoidable. The anisotropic TOV equation can then be used to bound the pressure anisotropy. The transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl--Bondi bound for perfect fluid stars. Finally we comment on the qualitative features of the equation of state that gravastar material must have if it is to do the desired job of preventing horizon formation.