The idea was elegant: take a BTZ black hole (the three-dimensional analog of a regular black hole) and smooth its horizon with a special function. The hope was that inside, the spacetime signature might change — time becoming space, and space becoming time. But the calculations showed otherwise.
Instead of a signature change, the geometry turned into a 'black trampoline' (black hole with a traversable throat). If you switch to the coordinates of an infalling observer, spacetime continues beyond the horizon: there lies a second region, an exact copy of the exterior. The minimal throat radius (the narrowest point) sits at the horizon, and the singularity disappears. This is not curvature leading nowhere, but a bridge between two worlds.
The authors computed the effective matter source that supports such a geometry and proved that all energy conditions are satisfied. Near the throat, spacetime becomes AdS₂ × S¹ — the product of two-dimensional anti-de Sitter space and a circle. Scalar perturbations are stable, but there is a peculiar Aretakis-type instability: the leading transverse derivative is conserved, while the next one grows linearly with time.
The work did not confirm the signature-change hypothesis, but it provided an exact recipe for constructing a traversable wormhole from a BTZ black hole. This is important for understanding quantum gravity and the thermodynamics of horizons.
The entropy of the throat of a BTZ black hole is proportional to the circumference of the throat, not the area, as in the four-dimensional case. In three dimensions, the horizon is a circle, not a sphere.
The idea of wormholes connecting different regions of space is familiar from the movie 'Interstellar', where heroes travel through a wormhole in search of a new home for humanity.