On the degrees of freedom of a semi-Riemannian metric

TL;DR

This paper demonstrates that any semi-Riemannian metric can be derived from a constant curvature metric through a deformation parametrized by a differential 2-form, elucidating the degrees of freedom involved.

Contribution

It establishes that semi-Riemannian metrics are obtainable via 2-form deformations from constant curvature metrics, clarifying their degrees of freedom.

Findings

Semi-Riemannian metrics have n(n-1)/2 degrees of freedom.

Any semi-Riemannian metric can be obtained as a 2-form deformation of a constant curvature metric.

The deformation is parametrized explicitly by a differential 2-form.

Abstract

A semi-Riemannian metric in a n-manifold has n(n-1)/2 degrees of freedom, i.e. as many as the number of components of a differential 2-form. We prove that any semi-Riemannian metric can be obtained as a deformation of a constant curvature metric, this deformation being parametrized by a 2-form