Not quite a black hole

Abstract

Astrophysical black hole candidates, although long thought to have a horizon, could be horizonless ultra-compact objects. This intriguing possibility is motivated by the black hole information paradox and a plausible fundamental connection with quantum gravity. Asymptotically free quadratic gravity is considered here as the UV completion of general relativity. A classical theory that captures its main features is used to search for solutions as sourced by matter. We find that sufficiently dense matter produces a novel horizonless configuration, the 2-2-hole, which closely matches the exterior Schwarzschild solution down to about a Planck proper length of the would-be horizon. The 2-2-hole is characterized by an interior with a shrinking volume and a seemingly innocuous timelike curvature singularity. The interior also has a novel scaling behavior with respect to the physical mass of the 2-2-hole. This leads to an extremely deep gravitational potential in which particles get efficiently trapped via collisions. As a generic static solution, the 2-2-hole may then be the nearly black endpoint of gravitational collapse. There is a considerable time delay for external probes of the 2-2-hole interior, and this determines the spacing of echoes in a post-merger gravitational wave signal.