A perspective on Black Hole Horizons from the Quantum Charged Particle

Understand

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.