The true radiation gauge for gravity

Abstract

Corresponding to the similarity between the Lorentz gauge ${\partial }_{\mu }{A}^{\mu }=0$ in electrodynamics and $g^{\mu \nu }{\Gamma }_{\mu \nu }^{\rho }=0$ in gravity, we show that the counterpart of the radiation gauge ${\partial }_i{A}^i=0$ is $g^{ij}{\Gamma }_{ij}^{\rho }=0$, in stead of other forms as discussed before. Particularly: 1) at least for a weak field, $g^{ij}{\Gamma }_{ij}^{\rho }=0$ 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 $g^{ij}{\Gamma }_{ij}^{\rho }=0$ 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

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• Do gluons carry half of the nucleon momentum?

Cited by in corpus (1)

• Physical decomposition of the gauge and gravitational fields