The magnetic dipole interaction in Einstein-Maxwell theory

TL;DR

This paper derives exact solutions in Einstein-Maxwell theory for configurations of magnetic dipoles and spinning magnets, revealing the nature of spin-spin interactions and their classical analogs.

Contribution

It provides new exact solutions for magnetic dipoles and spinning magnets in Einstein-Maxwell theory, elucidating their interaction forces.

Findings

Spin-spin force is opposite in sign to magnetic dipole force.

Classical value of magnetic dipole interaction is recovered in first approximation.

Solutions describe equilibrium configurations of massless magnetic and spinning particles.

Abstract

I derive an exact, static, axially symmetric solution of the Einstein-Maxwell equations representing two massless magnetic dipoles, and compare it with the corresponding solution of Einstein's equations for two massless spinning particles (see gr-qc/0201094). I then obtain an exact stationary solution of the Einstein-Maxwell equations representing two massless spinning magnets in balance. The conclusion is that the spin-spin force is analogous to the force between two magnetic dipoles, but of opposite sign, and that the latter agrees with the classical value in the first approximation.