On the Dirac operator for a test electron in a Reissner–Weyl–Nordström black hole spacetime

Research output: Contribution to journalArticlepeer-review


The present paper studies the Dirac Hamiltonian of a test electron with a domain of bi-spinor wave functions supported on the static region inside the Cauchy horizon of the subextremal RWN black hole spacetime, respectively inside the event horizon of the extremal RWN black hole spacetime. It is found that this Dirac Hamiltonian is not essentially self-adjoint, yet has infinitely many self-adjoint extensions. Including a sufficiently large anomalous magnetic moment interaction in the Dirac Hamiltonian restores essential self-adjointness; the empirical value of the electron’s anomalous magnetic moment is large enough. In the subextremal case the spectrum of the self-adjoint Dirac operator with anomalous magnetic moment is purely absolutely continuous and consists of the whole real line; in particular, there are no eigenvalues. The same is true for the spectrum of any self-adjoint extension of the Dirac operator without anomalous magnetic moment interaction, in the subextremal black hole context. In the extremal black hole sector the point spectrum, if non-empty, consists of a single eigenvalue, which is identified.

Original languageEnglish (US)
Article number15
JournalGeneral Relativity and Gravitation
Issue number1
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


  • Charged black holes
  • Dirac equation
  • Mathematical relativity
  • Reissner–Weyl–Nordström spacetime


Dive into the research topics of 'On the Dirac operator for a test electron in a Reissner–Weyl–Nordström black hole spacetime'. Together they form a unique fingerprint.

Cite this