6 - Stationary black holes

Summary

In 1931 Chandrasekhar established an upper bound for the mass of a cold self–gravitating star in thermal equilibrium (Chandrasekhar 1931a, 1931b). This leads one to consider the ultimate fate of a star which, having radiated all its thermo–nuclear energy, still has a mass beyond the critical limit (a few solar masses). Once the nickel and iron core has been formed, there exists no possibility for any further nuclear reactions; the core must therefore undergo gravitational collapse. The collapse may cease by the time the core has reached nuclear densities, which leads to the formation of a neutron star, provided that the mass of the collapsing part lies below the critical value. If this is not the case, then nothing can prevent total gravitational collapse (Chandrasekhar 1939, Oppenheimer and Snyder 1939, Oppenheimer and Volkoff 1939), resulting in the formation of a black hole (Wheeler 1968; see Israel 1987 for a historical review).

Birkhoff's theorem (Birkhoff 1923), which states that a spherically symmetric spacetime is locally isometric to a part of the Schwarzschild–Kruskal metric (Kruskal 1960), yields a significant simplification in the discussion of the spherically symmetric collapse scenario (Harrison et al. 1965). However, in order to treat more general situations, one has to find the generic features of gravitational collapse in general relativity. This was achieved by Geroch, Hawking, Penrose and others in the late sixties and early seventies (Hawking and Penrose 1970; see also Hawking and Ellis 1973, Clarke 1975, 1993): The singularity theorems show that - in contrast to Newtonian gravity - deviations from spherical symmetry, internal pressure or rotation do not prevent the formation of a singularity.