The (Weak) Gravitational Field of a Dirac Monopole

TL;DR

This paper investigates the gravitational effects of a Dirac monopole within the weak-field approximation of general relativity, emphasizing the dominant role of the Dirac string's energy in its gravitational signature.

Contribution

It demonstrates how the gravitational field of a Dirac monopole can be modeled using weak-field GR, highlighting the significance of the Dirac string's energy as the primary gravitational source.

Findings

The Dirac string's gravitational effect dominates the monopole's field.

The weak-field limit matches solutions associated with the monopole's magnetic field and the string's energy.

The primary gravitational contribution is from a line of energy along the string.

Abstract

We establish the gravitational detectability of a Dirac monopole using a weak-field limit of general relativity, which can be developed from the Newtonian gravitational potential by including energy as a source. The resulting potential matches (by construction) the weak-field limit of two different solutions to Einstein's equations of general relativity: one associated with the magnetically monopolar spray of field lines emerging from the half-infinite solenoid that makes up the Dirac monopole, the other associated with the field-energetic source of the solenoid itself (the Dirac string). The string's gravitational effect dominates, and we suggest that the primary strong-field contribution of the Dirac configuration is that of a half-infinite line of energy, whose GR solution is known.