General Solution for Self-Gravitating Spherical Null Dust

摘要

We find the general solution of equations of motion for self-gravitatingspherical null dust as a perturbative series in powers of the outgoing matterenergy-momentum tensor, with the lowest order term being the Vaidya solutionfor the ingoing matter. This is done by representing the null-dust model as a2d dilaton gravity theory, and by using a symmetry of a pure 2d dilaton gravityto fix the gauge. Quantization of this solution would provide an effectivemetric which includes the back-reaction for a more realistic black holeevaporation model than the evaporation models studied previously.