In the previous chapter we compiled the basic geometric identities for stationary and axisymmetric spacetimes. We shall now use these relations to derive the Kerr metric. Although we have to postpone the general definitions of black holes and event horizons to a later chapter, we feel that this is the right time to present the Kerr solution. As we shall argue when going into the details of the uniqueness theorems, the Kerr metric occupies a distinguished position amongst all stationary solutions of the vacuum Einstein equations.

The nonrotating counterpart of the Kerr solution was found by Schwarzschild (1916a, 1916b) immediately after Einstein's discovery of general relativity (Einstein 1915a, 1915b). In contrast to this, it took almost half a century until Kerr (1963) was eventually able to derive the first asymptotically flat exterior solution of a rotating source in general relativity. As is well known, both the Schwarzschild and the Kerr metric have charged generalizations, which were found by Reissner (1916) and Nordstrom (1918) in the static case, and by Newman et al. (1965) in the circular case.

The fact that it was not until 1963 that the Kerr metric was discovered reflects the difficulties of its derivation. As was pointed out by Chandrasekhar (1983), this does, however, not imply that “there is no constructive analytic derivation of the Kerr metric that is adequate in its physical ideas…” (Landau and Lifshitz 1971). In fact, the derivation of the Kerr solution appears fairly transparent when based on a discussion of the general properties of stationary and axi-symmetric spacetimes.