Black hole horizons and quantum charged particles

TL;DR

This paper draws an analogy between black hole apparent horizons and quantum charged particles on a surface, revealing insights into the spectral properties of black hole horizons through quantum mechanics.

Contribution

It introduces a novel analogy linking black hole horizon stability to quantum particle spectra, providing new perspectives on MOTS spectral analysis.

Findings

Spectral problem of MOTS stability resembles quantum particle Hamiltonian.

Negative fine-structure constant analogy offers new insights into black hole horizons.

Quantum spectrum analysis informs the understanding of black hole apparent horizons.

Abstract

We point out a structural similarity between the characterization of black hole apparent horizons as stable marginally outer trapped surfaces (MOTS) and the quantum description of a non-relativistic charged particle moving in given magnetic and electric fields on a closed surface. Specifically, the spectral problem of the MOTS-stability operator corresponds to a stationary quantum particle with a formal fine-structure constant $\alpha$ of negative sign. We discuss how such analogy enriches both problems, illustrating this with the insights into the MOTS-spectral problem gained from the analysis of the spectrum of the quantum charged particle Hamiltonian.