The physical gravitational degrees of freedom

TL;DR

This paper derives general relativity as a theory of evolving 3D conformal geometries based on principles of relationalism and change, revealing the fundamental symmetry principles underlying gravitational degrees of freedom.

Contribution

It introduces a new derivation of GR from relational principles, identifying the true physical gravitational degrees of freedom as arising from fundamental symmetries.

Findings

GR obtained in the CMC gauge and Hamiltonian form

Equations used in York's conformal technique derived from principles

Gravitational degrees of freedom linked to fundamental symmetries

Abstract

When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dimensional conformal Riemannian geometries obtained by imposing two general principles: 1) time is derived from change; 2) motion and size are relative. We write down an explicit action based on them. We obtain not only GR in the CMC gauge, in its Hamiltonian 3 + 1 reformulation but also all the equations used in York's conformal technique for solving the initial-value problem. This shows that the independent gravitational degrees of freedom obtained by York do not arise from a gauge fixing but from hitherto unrecognized fundamental symmetry principles. They can therefore be identified as the long-sought Hamiltonian physical gravitational degrees of freedom.