Some remarks on radiation gauges in general relativity

We prove that it is possible to specify the shift vector field for a given foliation in such a way as to provide automatically the transverse-traceless part of the second fundamental form K associated with the slices of the foliation. We interpret this particular specification as providing a simple way for characterizing the dynamical degrees of freedom of the gravitational field. The resulting gauge is not the minimal distortion gauge devised by Smarr and York. In numerical relativity it permits the maintenance in time of the difference equations associated with the divergence constraint.