Embedding G\"{o}del's universe in five dimensions

TL;DR

This paper explicitly constructs a global embedding of G"odel's universe into a five-dimensional Ricci-flat manifold with a non-Lorentzian signature, demonstrating the application of the Campbell-Magaard theorem.

Contribution

It provides the first explicit global embedding of G"odel's universe into a five-dimensional Ricci-flat space with non-Lorentzian signature.

Findings

Embedding space is Ricci-flat with signature (++--)

Embedding of G"odel's universe is explicit and global

Supports Campbell-Magaard theorem application

Abstract

According to the Campbell-Magaard theorem, any analytical spacetime can be locally and analytically embedded into a five-dimensional pseudo-Riemannian Ricci-flat manifold. We find explicitly this embedding for Godel's universe. The embedding space is Ricci-flat and has a non-Lorentzian signature of type (++--). We also show that the embedding found is global.