A rotating black hole is like a whirlpool in a river — spacetime swirls around it, dragging along everything nearby. In some gravity theories, this whirlpool also includes an extra field — a vector field. At each point, it has a direction and a length, like a compass needle. The authors asked: can such a needle keep a constant length throughout the space around a rotating hole?

It turns out, no. The first obstacle arises right at the poles — where the rotation axis pierces the event horizon (the surface from which nothing can escape). At these points, any smooth field inheriting the hole's symmetries is forced to vanish. If the field is required to have a constant nonzero length, it simply cannot be smooth — a discontinuity appears. It's like trying to comb a sphere evenly: a cowlick is inevitable.

The authors applied these general conclusions to a specific theory — Einstein gravity with an extra 'bumblebee' field that breaks Lorentz symmetry. They took a three-parameter family of solutions and found that on the rotation axes, the field is not smooth due to its constant nonzero norm, and the varying conicity leads to genuine curvature singularities. Spacetime tears there.

So constancy of a vector field and rotation don't mix well. The spacetime whirlpool either forces the field to vanish at the poles or tears the very fabric of the universe.