A Classical Firewall Transformation as a Canonical Transformation

TL;DR

This paper critically examines 't Hooft's firewall transformation, revealing inconsistencies in its classical assumptions and proposing a corrected classical analog that suggests firewalls persist even after quantization.

Contribution

The paper identifies flaws in the classical foundation of 't Hooft's firewall transformation and introduces a revised classical model for spherical shells that challenges the firewall removal claim.

Findings

The original limiting procedure is inconsistent.

A new classical analog for the firewall transformation is proposed.

Firewalls are likely to persist after quantization.

Abstract

The firewall transformation put forward by 't Hooft in recent years has made ambitious claims of solving the firewall problem and the black hole information paradox while maintaining unitary evolution. However, the theory has received limited attention from the community, especially in regards to its foundations in purely classical gravitational physics. This paper investigates the underlying assumptions of 't Hooft's firewall transformation before quantization. We find that the limiting procedure used by 't Hooft in order to obtain an identification of the quantum operators for ingoing and outgoing particles near a black hole is not consistent. We propose a correction, which involves a more relaxed approximation regime. In the new approximation regime, we find a new classical analog for the firewall transformation for spherical shells, which allows evolving the spherical shells' dynamics past their point of collision. In the classical theory, no firewall is removed, as both ingoing and outgoing matter is present on every spacelike hypersurface, and it does not appear that any firewalls will be removed after a canonical quantization.