Efforts to Prove the Cosmic Censor

Unlike the idealized OSD homogeneous collapse scenario, real stars have an inhomogeneous density, as well as non-zero pressures within them as they collapse. Moreover, stars also rotate. Does every massive star collapsing at the end of its life-cycle turn into a black hole, as the OSD case specifies? The CCC answers affirmatively, namely, that the singularity forming during collapse ends up being hidden within an event horizon, never to be seen by external observers.

In the 1980s, Andrzej Krolak and Richard Newman wrote a series of papers that tried formulating CCC mathematically rigorously and for possible proofs. In 1988, Newman and I wrote a paper formulating and proving a theorem that claimed a proof for censorship under a set of assumptions on the spacetime. However, we later realized that the assumptions used in the result we showed were too strong and probably not physically realistic. Thus even when the theorem proved alright, it could not be possibly regarded as a proof for CCC. Other similar attempts have been made too.

It was at this point that we realized we needed a further detailed investigation of gravitational collapse scenarios within the framework of Einstein’s theory of gravity, along the lines of the OSD work, but generalizing and choosing more physically realistic cases and scenarios. The OSD model uses very idealistic and over-simplified assumptions, mainly in order to solve Einstein’s complex system of equations. We needed to see whether in physically realistic cases the final fate of gravitational collapse would be a black hole or a naked singularity. In practical terms, this amounted to checking whether trapped surfaces and event horizons formed in more realistic collapses, and if so whether that was before or after the occurrence of the spacetime singularity. As we shall see, it is this latter factor that really decides whether the spacetime singularity of collapse will be naked or hidden and covered by the event horizon.

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