A Spacetime 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; 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.