No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

The Dirac point electron in zero-gravity Kerr–Newman spacetime

### Abstract

Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint and the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. The symmetry result extends to the Dirac operator on a generalization of the zero-G Kerr–Newman spacetime with different electric-monopole/magnetic-dipole-moment ratios.

© 2015 AIP Publishing LLC

Received 15 November 2014
Accepted 04 April 2015
Published online 28 April 2015

Acknowledgments:
We thank Friedrich Hehl for his comments on an earlier version of this paper and for bringing several references to our attention. We are also thankful to the anonymous referee for constructive comments and for pointing out Ref.
15
.

Article outline:

I. INTRODUCTION
II. FORMULATION OF THE MAIN RESULTS
A. Dirac’s equation for a point electron on zero-*G* Kerr spacetimes equipped with electromagnetic Sommerfeld fields of arbitrary *Iπa*/*Q*-ratio
1. Zero-*G* Kerr spacetimes
2. Zero-G Kerr-Newman spacetimes
3. Generalizations of z*G*KN spacetimes to arbitrary charge and current
4. The Dirac equation on electromagnetic spacetimes: Cartan’s frame method
5. Frame formulation of the Dirac equation on z*G*K spacetimes featuring generalized electromagnetic Sommerfeld fields with arbitrary *Iπa*/*Q*-ratio
6. A Hilbert space for
B. Statement of the main theorems
1. Symmetry of the spectrum of the Dirac Hamiltonians
2. Essential self-adjointness of the Dirac Hamiltonian on z*G*KN
3. The continuous spectrum of the Dirac Hamiltonians on z*G*KN
4. The point spectrum of the Dirac Hamiltonian on z*G*KN
III. PROOF OF THEOREM 2.8 (SYMMETRY OF THE ENERGY SPECTRUM)
IV. PROOF OF THEOREM 2.9 (ESSENTIAL SELF-ADJOINTNESS (*Q* = *Iπa*))
V. CHANDRASEKHAR–PAGE–TOOP SEPARATION-OF-VARIABLES (*Q* = *Iπa*)
A. The Chandrasekhar ansatz
VI. PROOF OF THEOREM 2.10 (CONTINUOUS SPECTRUM OF ON z*G*KN)
VII. PROOF OF THEOREM 2.11 (POINT SPECTRUM OF ON z*G*KN)
A. The Prüfer transform
B. The realm of *L*
^{2} solutions
C. Existence of heteroclinic orbits connecting the two saddles
1. Flow on a finite cylinder
2. Connecting orbits and corridors
3. Parameter-dependent flows
4. Winding number of orbits and corridors
5. Continuity argument for existence of saddles connectors
6. Existence of saddles connectors for the Θ equation
7. Topology of the nullclines
8. Explicit solutions of the Θ equation
9. Existence of corridors with unequal winding number
10. Existence of saddles connectors for the Ω equation
11. Topology of the nullclines
12. Existence of corridors with unequal winding number
13. The iteration argument
VIII. SUMMARY AND OUTLOOK

/content/aip/journal/jmp/56/4/10.1063/1.4918361

http://aip.metastore.ingenta.com/content/aip/journal/jmp/56/4/10.1063/1.4918361

Article metrics loading...

/content/aip/journal/jmp/56/4/10.1063/1.4918361

2015-04-28

2016-10-21

Full text loading...

###
Most read this month

Article

content/aip/journal/jmp

Journal

5

3

Commenting has been disabled for this content