Kerr-Newman solution as a Dirac particle

TL;DR

This paper demonstrates that the Kerr-Newman spacetime solution can be interpreted as a Dirac particle, linking spacetime geometry with electron-positron properties, including spin and charge, through topological and quantum considerations.

Contribution

It introduces a novel interpretation of the Kerr-Newman solution as a Dirac particle, connecting spacetime topology with quantum spin and particle states.

Findings

Kerr-Newman solution admits states with half-integer angular momentum.

States transform under 4pi rotations, indicating spinor behavior.

The solution's evolution follows the Dirac equation, modeling electron-positron systems.

Abstract

For m^2 < a^2 + q^2, with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr--Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown first that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Next, it is shown that due to the topological structure of the extended KN spacetime it does admit states with half-integral angular momentum. This last property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4pi rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.