The true radiation gauge for gravity

TL;DR

This paper introduces a true radiation gauge for gravity, analogous to the Lorentz gauge in electrodynamics, which fully fixes the gauge, isolates physical gravitational components, and aids in studying gravitational energy and radiation.

Contribution

It proposes a new gauge condition $g^{ij}\Gamma^\rho_{ij}=0$ for gravity, providing a complete gauge fixing and insights into gravitational energy and wave behavior.

Findings

The gauge fixes the gravitational field's physical components.

Non-dynamical components are solved instantaneously.

Gravitational radiation is generated by the transverse energy-momentum tensor.

Abstract

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.