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

Michael K.H. Kiessling; A. Shadi Tahvildar-Zadeh; Ebru Toprak

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

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

Michael K.H. Kiessling, A. Shadi Tahvildar-Zadeh, Ebru Toprak

School of Arts and Sciences, Mathematics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	American English
Article number	15
Journal	General Relativity and Gravitation
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s10714-021-02789-0
State	Published - Jan 2021

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Keywords

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

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

Cite this

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abstract = "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{\textquoteright}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.",

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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.

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KW - Dirac equation

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

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Keywords

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