At the center of attention is a monopole, a special clump of a non-Abelian field (a field where the order of operations changes the result), resembling a magnetic charge without a pair. In this work, it is placed in curved spacetime described by Einstein's equations with a Gauss-Bonnet addition (a correction important at small distances). The addition acts as a regulator: depending on its form, the monopole either remains smooth or hits a critical point.
The authors examined two variants of coupling the addition to the field.
For a large parameter value, the principal part of the equations degenerates at a critical radius. This is like the moment when ice turns into water — a geometric phase transition. Exponential coupling, on the other hand, smooths out all irregularities and prevents the equations from degenerating.
The most intriguing part is the physical meaning of the critical solution. Space seems to split into two regions: an outer one, where the familiar Einstein still works, and an inner one, where classical notions break down.
Thus, the monopole inadvertently outlines the boundary beyond which our usual clocks and rulers lose meaning.
The idea of the monopole dates back to Dirac, who showed that the existence of at least one such object in the Universe would explain why electric charge is always quantized.
In Peter Watts's novel Blindsight, alien probes use something like magnetic monopoles to manipulate spacetime.