14 - Black Holes and Singularities

Summary

Spherical Gravitational Collapse

One of the most remarkable predictions of general relativity is that, under extreme – but by no means unobtainable – conditions, gravitational collapse can lead inexorably to arbitrarily high densities and, ultimately, to a spacetime singularity. Gravitational collapse takes place when the internal pressure in a body (e.g., a star) is insufficient to counteract the inward pull of gravity. Since the pressure increases as the body contracts, one might expect that there will always come a point when this will be sufficient to prevent further contraction and that the star will settle down in some stable but denser state. This is indeed the case for a star of mass equal to that of the sun. The theory of stellar evolution tells us that such stars can reach a final equilibrium state as a white dwarf or a neutron star. However, for slightly larger stars, no such final equilibrium state is possible, and in such a case the star will contract beyond a certain critical point – the point of no return – where complete gravitational collapse leading to a spacetime singularity is inevitable.

In this section we restrict attention to the idealized case of spherically symmetric collapse, but, as we shall see later, the same phenomenon also occurs in a more general setting.

In order to gain an intuitive view of gravitational collapse, we first consider the case of Newtonian gravity.