An ordinary black hole resembles a funnel, at whose center spacetime plunges into a point — a singularity. There, density becomes infinite and the laws of physics break down. But what if, instead of a plunge, there were a smooth bottom inside?
The authors of the study constructed exactly such a model. They added to the Einstein equations a special field — a scalar triplet and an auxiliary sector that does not propagate on its own. With a spherically symmetric 'hedgehog' configuration, the solution yields a black hole with regular geometry — its curvature is finite everywhere. Inside, a core forms that resembles de Sitter space (expanding, like our Universe on large scales), and from the outside, the hole is nearly indistinguishable from a Schwarzschild one. The first difference appears only in corrections of order $r^{-4}$, that is, very close to the horizon.
The researchers checked the thermodynamics of these objects and their behavior in strong fields. It turned out that the regularity is purely geometric: curvature invariants do not blow up, although the material field itself at the center is not entirely smooth. This resembles a situation where a rubber ball is squeezed but not to a point — the surface remains intact, even if there are microcracks inside.
This approach requires no exotic matter or quantum corrections — only classical fields subject to certain constraints. Perhaps this is how nature avoids singularities, replacing them with finite 'cores'.
The term 'black hole' was coined by John Wheeler in 1967, but the idea of objects from which light cannot escape dates back to John Michell in 1783.
In Michael Crichton's novel 'Sphere', the protagonists find a perfectly smooth object of unknown origin — perhaps an artifact of a civilization that learned to create regular black holes.