Non-singular black hole without anisotropic fluids

We construct static spherically-symmetric solutions to general relativity in the presence of a cosmological constant and phantom Chaplygin gas. We find ultra-compact solutions that mimic black holes right down to the event horizon, but are nonsingular everywhere and have no layers or junctions. These gravastar solutions evade the Buchdahl-Bondi bound and are interesting because of their smooth interiors. Previous gravastar solutions require use of an anisotropic thin shell, whereas our model requires only phantom Chaplygin gas, a perfect fluid. We evade the Cattoen--Faber--Visser theorem because the Chaplygin gas is superluminal, defining a causal-frame metric that is geodesically complete despite the pressure pole of the Einstein-frame metric. Geodesics of the Einstein-frame metric reach future infinity of the causal-frame metric without ever crossing the surface of the gravastar, faithfully behaving as they are seen from the outside a black hole. Phantom Chaplygin gas was previously thought to be pathological due to super-luminality, pressure divergences, and violation of the null energy condition. In fact, all of these features are non-pathological. Furthermore, the Hamiltonian is bounded below and above.