21 - The Kerr metric

Summary

This is an encyclopaedia of basic knowledge about the Kerr metric and related topics. It includes, among other things, the original Kerr derivation from Einstein’s equations via the Kerr–Schild metrics, the Carter derivation from the separability of the Klein–Gordon equation (a by-product thereof is the generalisation to nonzero cosmological constant), the derivation (with illustrations) of the formulae for the event horizons and stationary limit hypersurfaces, the derivation of Carter’s fourth first integral of geodesic equations, the discussion of properties of general geodesics and of geodesics in the equatorial plane, the maximal analytic extension by Boyer and Lindquist, the Penrose process of extracting angular momentum from a rotating black hole and the Bardeen proof of existence of locally nonrotating observers in a stationary-axisymmetric spacetime.