General relativity is a highly nonlinear model, and as such, its 3+1D version is usually too complicated to analyze in detail.
It is also the action for Non-critical string theory and dimensional reduction of higher-dimensional model.
The matter field only couples to the causal structure, and in the light-cone gauge ds2 = − e2ρ du,dv, has the simple generic form with a factorization between left- and right-movers.
The masslessness of the matter fields allow a black hole to completely evaporate away via Hawking radiation.
In fact, this model was originally studied to shed light upon the black hole information paradox.