True radiation gauge for gravity

Authors:
Publisher website
Google Scholar
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 $\partial${}iAi=0 is gij$\Gamma${}ij$\rho${}=0, instead of other forms as discussed before. Particularly, 1)~at least for a weak field, gij$\Gamma${}ij$\rho${}=0 fixes the gauge completely and picks out exactly the two physical components of the gravitational field; 2)~like A0, the nondynamical components h0$\mu${} are solved instantaneously; 3)~gravitational radiation is generated by the ``transverse'' part of the energy-momentum tensor, similar to the transverse current J$\rightarrow${}$\perp${}. This ``true'' radiation gauge gij$\Gamma${}ij$\rho${}=0 is especially pertinent for studying gravitational energy, such as the energy flow in gravitational radiation. It agrees with the transverse-traceless gauge for a pure wave, and reveals remarkably how the transverse-traceless gauge can be adapted in the presence of source.