  We find the general solution of equations of motion for self-gravitating
spherical null dust as a perturbative series in powers of the outgoing matter
energy-momentum tensor, with the lowest order term being the Vaidya solution
for the ingoing matter. This is done by representing the null-dust model as a
2d dilaton gravity theory, and by using a symmetry of a pure 2d dilaton gravity
to fix the gauge. Quantization of this solution would provide an effective
metric which includes the back-reaction for a more realistic black hole
evaporation model than the evaporation models studied previously.
