Talk: A perspective on black hole horizons from the quantum charged particle
By José Luis Jaramillo
We point out a formal similarity between the characterization of black hole apparent horizons in terms of light rays trapped in spacetime, on the one hand, and the quantum description of a non-relativistic charged particle moving in given magnetic and electric fields on a closed surface, on the other hand. Such quantum analogy may provide clues to the study of the spectrum of the relevant (non-selfadjoint) apparent-horizon stability operator, in comparison with the (selfadjoint) Hamiltonian of the charged particle. In particular, this might open an avenue to the spinorial treatment of apparent horizon stability and to the use of semiclassical tools to explore qualitative aspects of the black hole spectral problem. More generally, it offers a case study for spectral geometric analysis motivated from gravitation theory.