A General Relativistic Model for Magnetic Monopole-Infused Compact Objects

TL;DR

This paper develops a relativistic model for compact objects containing magnetic monopoles, deriving their internal structure and external spacetime, revealing that monopole-infused objects require negative internal pressure for equilibrium.

Contribution

It introduces a novel general relativistic solution for monopole-infused compact objects, incorporating magnetic monopoles into Einstein-Maxwell equations with explicit internal and external metric solutions.

Findings

Effective monopole magnetic field mass is three times the fluid mass.

Interior matter must have negative pressure for equilibrium.

Exterior spacetime matches a magnetic Reissner-Nordström metric.

Abstract

Emergent concepts from astroparticle physics are incorporated into a classical solution of the Einstein-Maxwell equations for a binary magnetohydrodynamic fluid, in order to describe the final equilibrium state of compact objects infused with magnetic monopoles produced by proton-proton collisions within the intense dipolar magnetic fields generated by these objects during their collapse. It is found that the effective mass of such an object's acquired monopolar magnetic field is three times greater than the mass of its native fluid and monopoles combined, necessitating that the interior matter undergo a transition to a state of negative pressure in order to attain equilibrium. Assuming full symmetry between the electric and magnetic Maxwell equations yields expressions for the monopole charge density and magnetic field by direct analogy with their electrostatic equivalents; inserting these into the Einstein equations then leads to an interior metric which is well-behaved from the origin to the surface, where it matches smoothly to an exterior magnetic Reissner-Nordstr\"om metric free of any coordinate pathologies. The source fields comprising the model are all described by simple, well-behaved polynomial functions of the radial coordinate, and are combined with straightforward regularity conditions to yield expressions delimiting several fundamental physical parameters pertaining to this hypothetical astrophysical object.