Conformal Superspace: the configuration space of general relativity

TL;DR

This paper demonstrates that conformal superspace is the natural configuration space for canonical general relativity by revealing an unexpected symmetry in the conformal method, leading to a unique evolution in this space.

Contribution

The authors prove that Einstein equations generate a unique curve in conformal superspace, confirming its role as the natural configuration space for general relativity.

Findings

Identification of an unexpected symmetry in the conformal method

Unique curve generation in conformal superspace from Einstein equations

Confirmation of conformal superspace as the natural configuration space

Abstract

It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the Einstein constraints has an unexpected extra symmetry. This allows us to complete the project. We show that given a point and a velocity in conformal superspace, the Einstein equations generate a unique curve in conformal superspace.