The no-hair theorem says black holes are simple. Mass, charge, spin — three numbers specify the entire object. Every stationary vacuum black hole is a Kerr solution. No exceptions, no variants, no choices. This is uniqueness: given the same parameters, there is one and only one black hole.
Eichhorn, Fernandes, and Marino show that uniqueness doesn't just fail beyond general relativity — it fails in a way that resembles condensed matter more than astrophysics. In a theory where a scalar field couples cubically to the Gauss-Bonnet invariant, the Kerr solution becomes unstable at high spin through two competing mechanisms: curvature-induced scalarization (the scalar field grows because curvature is strong) and spin-induced scalarization (the scalar field grows because the black hole is spinning fast). At large spin, both mechanisms operate simultaneously at the same sign of the coupling constant.
The result is not one alternative to Kerr, but multiple coexisting branches of black hole solutions. The system has continuous transitions between some branches and discontinuous transitions between others. This is a phase diagram: given the same mass and spin, several distinct black holes are valid solutions, distinguished by which symmetry-breaking pathway the scalar field took.
This is “strong” breaking of uniqueness. Weak breaking would be a single new solution replacing Kerr above some threshold. Strong breaking means the space of solutions itself acquires structure — branches, transitions, coexistence regions. The black hole becomes a system with phases, not a unique endpoint.
The analogy to condensed matter is exact, not metaphorical. Water has ice, liquid, and vapor phases under the same temperature and pressure at the triple point. These black holes have Kerr, curvature-scalarized, and spin-scalarized phases under the same mass and spin at certain parameter values. The universe might contain black holes that are identical in every externally measurable property but internally organized around different scalar field configurations — distinguishable only by their formation history.
Uniqueness was comforting because it meant black holes have no choices. Phase diagrams mean they do.