The true radiation gauge for gravity

Details The true radiation gauge for gravity The true radiation gauge for gravity

2010-06-20

arxiv.org/abs/1006.3927v3

Phys.Rev.D83:061501,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, no figure; significant revision, showing how the TT gauge can be adapted in the presence of source

Scientific paper

10.1103/PhysRevD.83.061501

Corresponding to the similarity between the Lorentz gauge $\partial_\mu A^\mu=0$ in electrodynamics and $g^{\mu\nu}\Gamma^\rho_{\mu\nu}=0$ in gravity, we show that the counterpart of the radiation gauge $\partial_iA^i=0$ is $g^{ij}\Gamma^\rho_{ij}=0$, in stead of other forms as discussed before. Particularly: 1) at least for a weak field, $g^{ij}\Gamma^\rho_{ij}=0$ fixes the gauge completely and picks out exactly the two physical components of the gravitational field; 2) like $A^0$, the non-dynamical components $h_{0\mu}$ are solved instantaneously; 3) gravitational radiation is generated by the "transverse" part of the energy-momentum tensor, similar to the transverse current $\vec J_\perp$. This true" radiation gauge $g^{ij}\Gamma^\rho_{ij}=0$ is especially pertinent for studying gravitational energy, such as the energy flow in gravitational radiation. It agrees with the transverse-traceless (TT) gauge for a pure wave, and reveals remarkably how the TT gauge can be adapted in the presence of source.

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