Gravitational Collapse: The Role of General Relativity1

Stars whose masses are of the same order as that of the sun (M ) can find a final equilibrium state either as a white dwarf or, apparently, (after collapse and ejection of material) as a neutron star. These matters have been nicely discussed in the lectures of Hewish and Salpeter. But, as they have pointed out, for larger masses no such equilibrium state appears to be possible. Indeed, many stars are observed to have masses which are much larger than M —so large that it seems exceedingly unlikely that they can ever shed sufficient material so as to be able to fall below the limit required for a stable white dwarf (∼1.3M : Chandrasekhar [1]) or neutron star (∼0.7M : Oppenheimer-Volkoff [2]) to develop. We are thus driven to consider the consequences of a situation in which a star collapses right down to a state in which the effects of general relativity become so important that they eventually dominate over all other forces. I shall begin with what I think we may now call the “classical” collapse picture as presented by general relativity. Objections and modifications to this picture will be considered afterwards. The main discussion is based on Schwarzschild’s solution of the Einstein vacuum equations. This solution represents the gravitational field exterior to a spherically symmetrical body. In the original Schwarzschild co-ordinates, the metric takes the familiar form