An imbedding of spacetimes

TL;DR

This paper demonstrates that all two-dimensional globally hyperbolic spacetimes with compact Cauchy surfaces can be causally embedded into the Einstein's static universe, establishing a conformal equivalence for such spacetimes.

Contribution

It introduces a method to embed and relate two-dimensional spacetimes to the Einstein's static universe, expanding understanding of their causal structures.

Findings

Two-dimensional spacetimes with compact Cauchy surfaces can be causally embedded into the Einstein's static universe.

All two-dimensional globally hyperbolic spacetimes are conformally equivalent to subsets of the Einstein's static universe.

Abstract

It is shown that any two-dimensional spacetimes with compact Cauchy surfaces can be causally isomorphically imbedded into the two-dimensional Einstein's static universe. Also, it is shown that any two-dimensional globally hyperbolic spacetimes are conformally equivalent to a subset of the two-dimensional Einstein's static universe.