Gravastar energy conditions revisited

TL;DR

This paper revisits the energy conditions for gravastar models, deriving bounds on their surface compactness and stability criteria based on the dominant energy condition and causality constraints.

Contribution

It provides new analytic bounds on gravastar surface compactness considering different exterior geometries and stability conditions, refining previous models.

Findings

Maximum surface compactness for Schwarzschild gravastars with stiff shells.

Allowed configurations include shells under pressure, tension, or dust, depending on the exterior geometry.

Causality constraints further restrict the parameter space of stable gravastar models.

Abstract

We consider the gravastar model where the vacuum phase transition between the de Sitter interior and the Schwarzschild or Schwarzschild-de Sitter exterior geometries takes place at a single spherical delta-shell. We derive sharp analytic bounds on the surface compactness (2m/r) that follow from the requirement that the dominant energy condition (DEC) holds at the shell. In the case of Schwarzschild exterior, the highest surface compactness is achieved with the stiff shell in the limit of vanishing (dark) energy density in the interior. In the case of Schwarzschild-de Sitter exterior, in addition to the gravastar configurations with the shell under surface pressure, gravastar configurations with vanishing shell pressure (dust shells), as well as configurations with the shell under surface tension, are allowed by the DEC. Respective bounds on the surface compactness are derived for all cases. We also consider the speed of sound on the shell as derived from the requirement that the shell is stable against the radial perturbations. The causality requirement (sound speed not exceeding that of light) further restricts the space of allowed gravastar configurations.