A perspective on Black Hole Horizons from the Quantum Charged Particle

TL;DR

This paper explores a novel mathematical connection between black hole horizon stability and quantum charged particles, proposing a spectral analysis approach that could advance understanding of black hole physics.

Contribution

It introduces a new perspective linking black hole horizon stability to quantum spectral problems, including an analyticity conjecture and potential semiclassical methods.

Findings

Spectral properties of black hole horizons relate to quantum charged particle spectra.

Proposes an analyticity conjecture on spectral dependence on a complex parameter.

Suggests new avenues for semiclassical and spinorial analysis of horizon stability.

Abstract

Black hole apparent horizons possess a natural notion of stability, whose spectral characterization can be related to the problem of the stationary quantum charged particle. Such mathematical relation leads to an "analyticity conjecture" on the dependence of the spectral properties on a complex "fine-structure-constant" parameter, that can reduce the study of the spectrum of the (non-selfadjoint) MOTS-stability operator to that of the (selfadjoint) Hamiltonian of the quantum charged particle. Moreover, this perspective might open an avenue to the spinorial treatment of apparent horizon (MOTS-)stability and to the introduction of semiclassical tools to explore some of the qualitative aspects of this black hole spectral problem.