Mass and radius of cosmic balloons.

Abstract

Cosmic balloons are spherical domain walls with relativistic particles trapped inside. We derive the exact mass and radius relations for a static cosmic balloon using Gauss-Codazzi equations. The cosmic balloon mass as a function of its radius, $M(R)$, is found to have a functional form similar to that of fermion soliton stars, with a fixed point at $\frac{2GM(R)}{R}\ensuremath{\simeq}0.486$, which corresponds to the limit of infinite central density. We derive a simple analytical approximation for the mass density of a spherically symmetric relativistic gas star. When applied to the computation of the mass and radius of a cosmic balloon, the analytical approximation yields fairly good agreement with the exact numerical solutions.