TY - JOUR

T1 - On the Dirac operator for a test electron in a Reissner–Weyl–Nordström black hole spacetime

AU - Kiessling, Michael K.H.

AU - Tahvildar-Zadeh, A. Shadi

AU - Toprak, Ebru

N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - Charged black holes

KW - Dirac equation

KW - Mathematical relativity

KW - Reissner–Weyl–Nordström spacetime

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U2 - https://doi.org/10.1007/s10714-021-02789-0

DO - https://doi.org/10.1007/s10714-021-02789-0

M3 - Article

SN - 0001-7701

VL - 53

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

IS - 1

M1 - 15

ER -