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The physical gravitational degrees of freedom

Edward Anderson·Julian Barbour·Brendan Z. Foster·Bryan Kelleher·Niall Ó Murchadha
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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.

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Edward Anderson, Julian Barbour, Brendan Z. Foster, Bryan Kelleher, Niall Ó Murchadha. 2005-08-09. The physical gravitational degrees of freedom. https://doi.org/10.1088/0264-9381%2F22%2F9%2F020

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