Naked Reissner-Nordstr\"{o}m Singularities and the Anomalous Magnetic Moment of the Electron Field

TL;DR

This paper demonstrates that incorporating an anomalous magnetic moment into the Dirac field allows for a consistent quantum theory on a naked Reissner-Nordström background, revealing potential exotic atomic states and black hole formation scenarios.

Contribution

It introduces a non-perturbative approach to quantize the Dirac field with anomalous magnetic moment on a naked Reissner-Nordström spacetime, avoiding boundary conditions at the singularity.

Findings

Well-defined quantum theory without boundary conditions

Existence of bound states for the Dirac equation

Implications for exotic atomic systems and black hole formation

Abstract

We study the problem of the quantization of the massive charged Dirac field on a naked Reissner-Nordstr\"{o}m background. We show that the introduction of an anomalous magnetic moment for the electron field allows a well--defined quantum theory for the one-particle Dirac Hamiltonian, because no boundary condition on the singularity is required. This means that would-be higher order corrections can play an essential role in determining physics on the naked Reissner-Nordstr\"{o}m background and that a non-perturbative approach is required. Moreover, we show that bound states for the Dirac equation are allowed. Various aspects of the physical picture emerging from our study are also discussed, such as the possibility to obtain exotic atomic systems, the formation of black holes by electronic capture and some interesting consistency problems involving quantum gravity.