Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background

1998/05/31 by Felix Finster, Joel Smoller, Shing-Tung Yau · 1 citation
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #math-ph #math.MP

paper · pdf · doi:10.1063/1.533234

published as J.Math.Phys. 41 (2000) 2173-2194 · 24 pages, 2 figures (published version)

arxiv created 2000/01/20 · openalex publication_date 2000/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner–Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.

Citations

• Universality and scaling in gravitational collapse of a massless scalar field
• Particle creation by black holes

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