The physical gravitational degrees of freedom

Details The physical gravitational degrees of freedom The physical gravitational degrees of freedom

2004-07-27

arxiv.org/abs/gr-qc/0407104v2

Class.Quant.Grav. 22 (2005) 1795-1802

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Replaced with published version (minor changes and added references)

Scientific paper

10.1088/0264-9381/22/9/020

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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