Generalized Effective Field Theory for Four-Dimensional Black Hole Evaporation

TL;DR

This paper develops a generalized effective field theory framework for analyzing four-dimensional black hole evaporation, incorporating non-local quantum effects and identifying a unique quantum state consistent with the Unruh state.

Contribution

It introduces a truncated effective action including Weyl tensor terms to model quantum stress tensors in black hole backgrounds, extending previous trace anomaly approaches.

Findings

Derived a 4th order equation for the stress tensor in black hole spacetime.

Found a static solution matching properties of the Unruh quantum state.

Demonstrated the role of additional non-local terms in semiclassical gravity.

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.