Gravitational radiation from Schwarzschild black holes: the second-order perturbation formalism

The perturbation theory of black holes has been useful recently for providing estimates of gravitational radiation from the black-hole collisions. Second-order perturbation theory, relatively undeveloped until recently, has proved to be important both for providing refined estimates and for indicating the range of validity of perturbation theory. Here we review the second-order formalism for perturbations of Schwarzschild spacetimes. The emphasis is on practical methods for carrying out the second-order computations of the outgoing radiation. General issues are illustrated throughout with examples from “close-limit” results, perturbation calculations in which black holes start from the small separation.