Black hole horizons and quantum charged particles

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.

arXiv comment5 pages, no figures

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Cited by in corpus (14)

• Energy scales and black hole pseudospectra: the structural role of the scalar product
• The existence and stability of marginally trapped surfaces
• Ultimate fate of apparent horizons during a binary black hole merger II: Horizons weaving back and forth in time
• Horizons in a binary black hole merger I: Geometry and area increase
• A perspective on Black Hole Horizons from the Quantum Charged Particle
• Symmetry and instability of marginally outer trapped surfaces
• Complex magnetic fields: An improved Hardy-Laptev-Weidl inequality and quasi-self-adjointness
• Horizon area bound and MOTS stability in locally rotationally symmetric solutions
• Eigenvalues of the MOTS stability operator for slowly rotating Kerr black holes
• Marginally Outer Trapped Tori in Black Hole Spacetimes
• Ultimate fate of apparent horizons during a binary black hole merger I: Locating and understanding axisymmetric marginally outer trapped surfaces
• On the Stability of MOTS
• The gravitational Field of a massless Particle on the Horizon of a stationary Black Hole
• Cylindrical first order superintegrability with complex magnetic fields