Effective Field Theory Description of Hawking Radiation

TL;DR

The paper develops a 3+1D effective field theory for Hawking radiation based on the trace anomaly, localized through a Riegert-type scalar-tensor action. By solving the resulting fourth-order scalar equation on a Schwarzschild background and imposing physically reasonable boundary conditions, the authors derive a unique Unruh-like semiclassical stress tensor with vanishing ingoing flux and finite outgoing Hawking flux, and they show there is no quantum hair in this framework. A sign issue in the predicted flux for conventional matter is discussed, with proposed remedies such as adding a nonlocal Weyl-squared term or choosing $b>0$. The work provides a tractable, closed-form description of Hawking radiation within an EFT that can be extended to time-dependent back-reaction, gravitational collapse, and inclusion of additional fields to ensure positivity of the flux.

Abstract

A study is made of Hawking radiation from four-dimensional black holes using effective field theory methods. The trace anomaly for the stress tensor in a general curved spacetime background is reproduced using Riegert's action. The semiclassical stress tensor is evaluated in a Schwarzschild background taking a time-independent limit for the quantum state. Imposing physical boundary conditions on an initial Cauchy surface leads to a unique state, analogous to the Unruh state with a vanishing ingoing flux and a finite outgoing flux. In particular, there is no sign of quantum hair arising from this nonlocal effective action.