  The general class of Robinson-Trautman metrics that describe gravitational
radiation in the exterior of bounded sources in four space-time dimensions is
shown to admit zero curvature formulation in terms of appropriately chosen
two-dimensional gauge connections. The result, which is valid for either type
II or III metrics, implies that the gravitational analogue of the
Lienard-Wiechert fields of Maxwell equations form a new integrable sector of
Einstein equations for any value of the cosmological constant. The method of
investigation is similar to that used for integrating the Ricci flow in two
dimensions. The zero modes of the gauge symmetry (factored by the center)
generate Kac's K_2 simple Lie algebra with infinite growth.
