Bardeen Spacetime with Charged Dirac Field

TL;DR

This paper explores soliton solutions involving a charged Dirac field coupled with Einstein gravity and the Bardeen magnetic monopole, revealing how the Bardeen field influences critical charges and solution types.

Contribution

It introduces the concept of an effective frequency to analyze frozen star solutions in the presence of a Bardeen field, expanding understanding of charged Dirac fields in curved spacetime.

Findings

Bardeen field modifies the critical charge of the Dirac field.

Frozen star solutions occur at zero effective frequency with large magnetic charge.

Effective frequency approaches zero even when the actual frequency does not.

Abstract

In this article, we investigate soliton solutions in a system involving a charged Dirac field minimally coupled to Einstein gravity and the Bardeen field. We analyze the impact of two key parameters on the properties of the solution family: the magnetic charge $p$ of the Bardeen field and the electric charge $q$ of the Dirac field. We discover that the introduction of the Bardeen field alters the critical charge of the charged Dirac field. In reference [1], solutions named frozen stars are obtained when the magnetic charge is sufficiently large and the frequency approaches zero. In this paper, we define an effective frequency and find that, when the magnetic charge is sufficiently large, a frozen star solution can also be obtained, at which point the effective frequency approaches zero rather than the frequency itself.