Gravastar solutions with continuous pressures and equation of state

We study the gravitational vacuum star (gravastar) configuration as proposed by Cattoen et al ( 2005 Class. Quantum Grav. 22 4189 ) in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure of Mazur and Mottola (2001 Preprint gr-qc/0109035, 2003 Proc. 6th Workshop on Quantum Field Theory Under the Influence of External Conditions (Oklahoma) (Princeton, NJ: Rinton), Preprint gr-qc/0405111 (2004 Proc. Natl Acad. Sci. 111 9545) is replaced by a continuous stress–energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial p r and tangential p t pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar ( Cattoen et al 2005 Class. Quantum Grav. 22 4189 ). Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.