  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
non-twisting but in general diverging and the corresponding solutions in
Einstein's theory form the Robinson-Trautman family together with a subset of
the 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 be always 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 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.
