An Exact, Coordinate Independent Classical Firewall Transformation

TL;DR

This paper develops a coordinate-independent, exact classical analog of 't Hooft's firewall transformation using ADM formalism and a model of null shells in a Schwarzschild background, clarifying its physical foundation.

Contribution

It introduces a precise, coordinate-independent classical firewall transformation within the ADM formalism, advancing the understanding of black hole information paradox solutions.

Findings

Reproduces the Dray-'t Hooft-Redmount formula at shell collision

Provides a classical, exact, coordinate-independent firewall transformation

Lays groundwork for future quantization of the model

Abstract

A proposal for resolving the black hole information paradox was recently put forward by 't Hooft in the form of his firewall transformation. Although this proposal has begun to gain some limited traction, its physical foundation is still somewhat obscure. Here we develop a classical Hamiltonian analog, which is oriented towards quantization, by using the canonical formalism developed by Arnowitt, Deser, and Misner (ADM). We use a model of two null, spherical shells in a Schwarzschild black hole background, and within our ADM formalism we are able to characterize the dynamics of the entire system, especially at the point of collision, and we reproduce the related Dray-'t Hooft-Redmount formula. Finally, we are able to find a classical analog for 't Hooft's firewall transformation. Unlike 't Hooft's firewall transformation and previous classical analogs, the classical firewall transformation we obtain is free from approximation and maintains the coordinate independence of the ADM formalism. We leave to future work the quantization of the theory.