A consistent description is possible for gravitationally collapsed bodies in General Relativity, in which collapse stops before the object reaches its gravitational radius. Non-singular solutions exist with the density reaching a maximum close to the surface and then decreasing towards the centre. While such solutions have been calculated in specific cases, a recent study (Entropy journal, special issue on Black Hole thermodynamics) establishes the general conclusion from re-analysing the classic Oppenheimer-Snyder (OS) 1939 modelling of a dust star contracting under its self-gravity. ie. as a spherical distribution of non-interacting dust particles.
Though that article On Continued Gravitational Contraction implied support for a black-hole solution, this re-analysis shows that the final OS density distribution accords with gravastar and other shell model solutions. The parallel Oppenheimer-Volkoff (OV) study of 1939 used the equation of state for a neutron gas, but considered only stationary solutions of the field equations. Recently the OV equation of state was found to permit solutions with minimal rather than maximal central density, and now a similar topology is found for the OS dust collapsar, in which a uniform dust-ball starts with large radius and collapses to a shell at the gravitational radius with density decreasing monotonically towards the centre. The OS dust model gave the first exact, time-dependent solution of the field equations and was at one time considered central in black-hole theory. Regarded as a limiting case of OV, it indicates the possibility of neutron stars of unlimited mass with a similar shell topology, termed ‘horizonless’ as they lack the ‘event horizon’ of black-hole theory.