Stringy Robinson-Trautman solutions

A class of solutions of the low-energy string theory in four dimensions is studied. This class admits a geodesic, shear-free null congruence which is nontwisting but in general diverging and the corresponding solutions in Einstein's theory form the Robinson-Trautman family together with a subset of Kundt's class. The Robinson-Trautman conditions are found to be frame invariant in string theory. The Lorentz Chern-Simons three-form of the stringy Robinson-Trautman solutions is shown to always be closed. The stringy generalizations of the vacuum Robinson-Trautman equation are obtained and three subclasses of solutions are identified. One of these subclasses exists, among all the dilatonic theories, only in Einstein's theory and in string theory. Several known solutions including the dilatonic black holes, the $\mathrm{pp}$ waves, the stringy $C$ metric, and certain solutions which correspond to exact conformal field theories are shown to be particular members of the stringy Robinson-Trautman family. Some new solutions which are static or asymptotically flat and radiating are also presented. The radiating solutions have a positive Bondi mass. One of these radiating solutions has the property that it settles down smoothly to a black hole state at late retarded times.