Generalized Effective Field Theory for Four-Dimensional Black Hole Evaporation

The quantum induced stress tensor of 3+1-dimensional Einstein gravity, with conformally coupled matter, is studied in an effective field theory approach. In this context, Riegert's non-local effective action is sufficient to reproduce the trace anomaly in curved spacetime but in general the effective action can include additional non-local but scale invariant terms that influence the semiclassical physics without affecting the trace anomaly. Here, a truncated model, with only one additional term involving the square of the Weyl tensor, is used to find the induced stress tensor in a black hole background. With suitable physical conditions, a solution of the resulting 4th order equations leads, in a static limit, to a unique quantum state matching expected properties of the Unruh state.