General Solution for Self-Gravitating Spherical Null Dust

TL;DR

This paper derives a general perturbative solution for self-gravitating spherical null dust using 2D dilaton gravity, extending the Vaidya solution to include back-reaction effects relevant for black hole evaporation.

Contribution

It introduces a novel perturbative approach to solve for self-gravitating null dust in spherical symmetry using 2D dilaton gravity, enabling analysis of back-reaction in black hole models.

Findings

Provides a general solution series for null dust equations of motion.

Connects the solution to the Vaidya spacetime at lowest order.

Lays groundwork for quantization to include back-reaction effects.

Abstract

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.