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Generally, magnetic monopoles searches assume it has a mass. And that introduces gravity into the game. But, my question rough is:

Why should a magnetic monopole have a mass or any other gravitational/particle physics property if generally speaking they are topological in nature? Does it means magnetic monopoles also gravitate even if considered topological defects?

Related to this question: if magnetic monopoles do gravitate, what kind of "particle properties" do they have beyond mass? Helicity? Chirality? Spin?

In summary: why a (gauge) magnetic monopole should/could have mass and any other particle physics property like angular momentum (spin), electric charge (becoming a dyon), helicity or chirality, weak charge, color, etc? Does it extend as well to gravitational monopoles with NUT charges or similar?

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Why are we looking for magnetic monopoles to start with? Answer: because they fulfill symmetry requirements in the Maxwell equations. Why do we use Maxwell's equations? Answer: because they describe all the data we have for electricity , magnetism, and electromagnetism.

They fit a seen symmetry between electric and magnetic fields beautifully , for example the dipoles of these fields:

dipoles

The problem is experimental, there are point electric charges, there are no point magnetic charges in our classical experiments.

When quantum electrodynamics was introduced in the study of elementary particle physics, the problem appears there: there are point charges, all elementary particles that are charged have mass, spin and point charges, but there are no elementary particles with magnetic point charges, as can be verified in the table.

elem

Please note that all the particles in the table are backed by a plethora of experimental data. There are electric poles, but no magnetic poles particles.

Theoretical physicist work with various models that incorporate symmetries, and the symmetries would require for magnetic monopoles to exist. The way out for phenomenology is to give them such high masses that they would not be detectable in accelerator experiments, and are made to disappear due to large masses in various theories where they have to appear by symmetry.

I have made this small review in order to point out that the symmetry that asks for magnetic monopoles, will be a symmetric theory to the charge monopoles, as far as spin and mass and gravitational behavior goes. They are not searched out of a la cart theories, but as a necessary object that must appear from the field theory explaining the standard model data, so it has to be pushed to high masses. The behavior with other forces has to be symmetric with the behavior of charged monopoles/particles.

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A topological magnetic monopole is a stable non-vacuum solution to the field equations of a gauge theory. The mass of a magnetic monopole is the integral of the energy density of this field configuration over all space; for a true soliton solution this is finite. As the solution has a non-zero energy, it therefore couples to a gravitational field.

Properties of soliton solutions such as spin, electric charge etc. can be determined by considering the relevant conserved currents in the field theory describing the monopole.

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