On the Dirac operator for a test electron in a ReissnerWeylNordström black hole spacetime
Abstract
The present paper studies the Dirac Hamiltonian of a test electron with a domain of bispinor 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 selfadjoint, yet has infinitely many selfadjoint extensions. Including a sufficiently large anomalous magnetic moment interaction in the Dirac Hamiltonian restores essential selfadjointness; the empirical value of the electron's anomalous magnetic moment is large enough. In the subextremal case the spectrum of the selfadjoint 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 selfadjoint 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 nonempty, consists of a single eigenvalue, which is identified.
 Publication:

General Relativity and Gravitation
 Pub Date:
 January 2021
 DOI:
 10.1007/s10714021027890
 arXiv:
 arXiv:2009.07358
 Bibcode:
 2021GReGr..53...15K
 Keywords:

 ReissnerWeylNordström spacetime;
 Charged black holes;
 Dirac equation;
 Mathematical relativity;
 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 Mathematics  Spectral Theory
 EPrint:
 21 pages