The true radiation gauge for gravity

Abstract

Corresponding to the similarity between the Lorentz gauge $\partial_μA^μ=0$ in electrodynamics and $g^{μν}Γ^ρ_{μν}=0$ in gravity, we show that the counterpart of the radiation gauge $\partial_iA^i=0$ is $g^{ij}Γ^ρ_{ij}=0$, in stead of other forms as discussed before. Particularly: 1) at least for a weak field, $g^{ij}Γ^ρ_{ij}=0$ fixes the gauge completely and picks out exactly the two physical components of the gravitational field; 2) like $A^0$, the non-dynamical components $h_{0μ}$ 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 $g^{ij}Γ^ρ_{ij}=0$ 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.

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