An Introduction to General Relativity

NO SINGLE theoretical development in the last three decades has had more influence on gravitational theory than the discovery of the Kerr solution in 1963. The Kerr metric is a solution of the vacuum field equations. It is a generalization of the Schwarzschild solution, and represents the gravitational field of a special configuration of rotating mass, much as the external Schwarzschild solution represents the gravitational field of a spherical distribution of matter.

However, unlike the Schwarzschild case, no simple non-singular fluid ‘interior’ solution is known to match onto the Kerr solution. There is, nevertheless, no reason a priori why such a solution shouldn't exist.

Fortunately such speculations are in some respects beside the point, since the real interest in the Kerr solution for many purposes is its characterization of the final state of a black hole, after the hole has had the opportunity to ‘settle down’ and shed away (via gravitational radiation and other processes) eccentricities arising from the structure of the original body that formed the black hole.

To put the matter another way, suppose someone succeeded in exhibiting a good fluid interior for the Kerr metric. Well, that would be in principle very interesting; but there is no reason to believe that naturally occurring bodies (e.g. stars, galaxies, etc.) would tend to fall in line with that particular configuration.