Hawking radiation as instantons

TL;DR

This paper proposes a novel interpretation of Hawking radiation as instanton tunneling, offering a potential non-perturbative framework to address the black hole information loss paradox.

Contribution

It introduces a new instanton-based approach to describe Hawking radiation, bridging perturbative and non-perturbative regimes, and aims to shed light on the information loss problem.

Findings

Hawking radiation can be described by a family of instantons.

The instanton action depends only on the areal entropy difference.

The approach connects with existing perturbative methods in the appropriate limit.

Abstract

There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking's original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the end-stage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. We study instantons of a massless scalar field in Einstein gravity. We consider a complex-valued instanton that connects an initial pure black hole state to a black hole with a scalar field that represents the Hawking radiation at future null infinity, where its action depends only on the areal entropy difference. By comparing it with several independent approaches to Hawking radiation in the perturbative limit, we conclude that Hawking radiation may indeed be described by a family of instantons. Since the instanton approach can describe non-perturbative processes, we hope that our new interpretation and holistic method may shed lights on the information loss problem.