On the integrability of spherical gravitational waves in vacuum

Abstract

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.