A space-time in toroidal coordinates

Abstract

We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; and an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter space-time. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of Λ. © 2003 American Institute of Physics.