Why a Rotating Black Hole Can't Stand Still express
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.
Original abstract
as written by the authors arXiv:2607.17223
We establish two obstructions to globally regular rotating constant-norm vector vacua. At an axial fixed point of a regular nondegenerate bifurcate Killing horizon, horizon-boost and axial invariance force every smooth symmetry-inheriting one-form to vanish, contradicting a strictly nonzero constant norm. Independently, varying axial conicity produces an orthonormal curvature component diverging as the inverse proper distance and precludes a \(C^2\) extension. Applied to a three-parameter Kerr--disformal family in Einstein--bumblebee gravity, these results reveal a nonsmooth bumblebee one-form, while direct calculation shows that the Kretschmann scalar diverges as the inverse square of the transverse proper distance to either open exterior axis. Even the distinguished nonextremal branch selected by nonpolar outer-horizon regularity is therefore an exact nonpolar rotating exterior solution, not a globally regular isolated black hole. Together, these field- and metric-level obstructions provide a two-pronged no-go framework for globally regular rotating constant-norm vector vacua.
The 'bumblebee' field is named so because in particle physics there are hypothetical particles, bumblebees, whose existence would seem to be forbidden by conservation laws, but they still 'fly' due to spontaneous symmetry breaking — like a bumblebee that, according to aerodynamics, shouldn't fly, but does.
In Stanislaw Lem's novel 'Solaris', the planet's ocean violates the usual laws of physics — somewhat like the bumblebee field, which changes the rules of the game in gravity.