Gravitational Collapse of a Dust Cloud and the Cosmic Censorship Conjecture

Abstract

O. Tolman found in 1934 a class of solutions of Einstein’s equations which represent inhomogeneous spherically symmetric dust clouds (Tolman, 1934). In 1939 Oppenheimer and Snyder studied, as an idealized model of gravitational collapse (Oppenheimer and Snyder, 1939), the special case of Tolman’s class of solutions which corresponds to a homogeneous spherical dust cloud. They analyzed the behaviour of the outgoing light rays and were thus led to the black hole concept. The Oppenheimer-Snyder study, although treating only a very special case, was highly important for providing the intuition which guided the approach to more general problems; the concept of a trapped surface plays a central role in the Penrose-Hawking singularity theorems (Hawking and Ellis, 1973). Then, a conjecture was introduced, derived again from the Oppenheimer-Snyder example, namely that no singularities which are visible from infinity can develop from regular initial data (Hawking and Ellis, 1973). This is the weaker form of what is now called “the cosmic censorship conjecture”. There is a number of important results, among them the area theorem of black holes (Hawking and Ellis, 1973), which assume the truth of this conjecture. Finally, Penrose (1979) introduced a stronger form of the cosmic censorship conjecture which states that any singularities that arise from regular initial data are not even locally visible. This stronger conjecture is verified in the Oppenheimer-Snyder example.