Diagonalization of the metric of a Lorentzian 3-manifold

TL;DR

This paper proves that every smooth Lorentzian 3-manifold can be locally represented with a diagonal metric form using the method of moving frames, simplifying the analysis of such manifolds.

Contribution

It introduces a technique to diagonalize the metric of Lorentzian 3-manifolds globally using moving frames, a novel approach in differential geometry.

Findings

Every smooth Lorentzian 3-manifold admits a diagonal metric form.

The proof employs the method of moving frames.

The result simplifies the study of Lorentzian 3-manifolds.

Abstract

We study the problem of diagonalization of the metric of 3-dimensional Lorentzian manifold. Applying the technique of moving frames, we prove that every smooth Lorentzian 3-manifold admits an atlas in which the metric assumes a diagonal form.