Generalized Effective Field Theory for Four-Dimensional Black Hole Evaporation

TL;DR

The paper addresses semiclassical black hole evaporation by extending the Riegert non-local action with a scale-invariant Weyl^2 term and localizing it with two auxiliary scalars. This yields a fourth-order, linear yet covariant system that remains tractable within an effective field theory and reproduces the trace anomaly. In a Schwarzschild background, the authors derive a unique, horizon-regular induced stress tensor that corresponds to an Unruh-like vacuum with a finite outgoing flux, aligning with Hawking luminosity once a free coupling is fixed. The work demonstrates that deterministic semiclassical dynamics can emerge without resorting to exotic matter content, while highlighting that further conformal invariants could refine the asymptotics and motivate future time-dependent studies of evaporation.

Abstract

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.