Entropy of the Information Retrieved from Black Holes

TL;DR

This paper explores how quantum effects, specifically the Quantum Zeno Effect, can resolve divergences in black hole information retrieval proposals, aligning the entropy with the Bekenstein-Hawking law.

Contribution

It introduces quantum considerations into existing black hole information proposals, demonstrating how the Quantum Zeno Effect regularizes entropy calculations.

Findings

Quantum Zeno Effect tames entropy divergences

Corrects entropy to match Bekenstein-Hawking law

Provides a quantum perspective on black hole information retrieval

Abstract

The retrieval of black hole information was recently presented in two interesting proposals in the 'Hawking Radiation' conference: a revised version by G. 't Hooft of a proposal he initially suggested 20 years ago and, a new proposal by S. Hawking. Both proposals address the problem of black hole information loss at the classical level and derive an expression for the scattering matrix. The former uses gravitation back reaction of incoming particles that imprints its information on the outgoing modes. The latter uses supertranslation symmetry of horizons to relate a phase delay of the outgoing wave packet compared to their incoming wave partners. The difficulty in both proposals is that the entropy obtained from them appears to be infinite. By including quantum effects into the Hawking and 't Hooft's proposals, I show that a subtlety arising from the inescapable measurement process, the Quantum Zeno Effect, not only tames divergences but it actually recovers the correct $1/4$ of the area Bekenstein-Hawking entropy law of black holes.