A Spacetime in Toroidal Coordinates
arXiv:gr-qc/0303110 · doi:10.1063/1.1580999
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; an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter spacetime. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of the cosmological constant.
to appear in J. Math. Phys