A perspective on Black Hole Horizons from the Quantum Charged Particle

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.

arXiv comment6 pages, no figures, contribution to the proceedings volume of the Spanish Relativity Meeting ERE2014: "Almost 100 years after Einstein Revolution", Valencia, Spain, 1-5 September 2014

References in corpus (3)

• Local existence of dynamical and trapping horizons
• Black hole horizons and quantum charged particles
• A Young-Laplace law for black hole horizons

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• Eigenvalues of the MOTS stability operator for slowly rotating Kerr black holes
• On the Stability of MOTS
• The gravitational Field of a massless Particle on the Horizon of a stationary Black Hole