Quantum Tunneling and Trace Anomaly

TL;DR

The paper addresses quantum corrections to Hawking radiation for the Schwarzschild black hole by developing a quantum Hamilton-Jacobi formulation within the tunneling framework. It expands the one-particle action in powers of $\hbar$ to obtain a corrected inverse temperature $\beta_{(corr.)}$ and corresponding entropy corrections, including a leading logarithmic term whose coefficient $\beta_1$ is tied to the trace anomaly. The authors show that these results are equivalent to Hawking's original path-integral computation with zeta-function regularization and reproduce one-loop backreaction effects, connecting the tunneling picture to the trace anomaly. A quantum-corrected Schwarzschild metric is derived from the corrected temperature and periodicity, providing a concrete realization of quantum backreaction at ${\cal O}(\hbar)$ and aligning with prior York-Lousto findings. Overall, the work clarifies the link between tunneling, trace anomalies, and backreaction in black-hole thermodynamics, and extends the semiclassical picture to include explicit quantum corrections.

Abstract

We compute the corrections, using the tunneling formalisim based on a quantum WKB approach, to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawking's original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.