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

TL;DR

This paper develops a second order perturbation formalism for Schwarzschild black holes, enhancing the accuracy of gravitational radiation estimates from black hole collisions and clarifying the limits of perturbation theory.

Contribution

It introduces a practical second order perturbation framework for Schwarzschild black holes, expanding the tools for gravitational wave predictions.

Findings

Second order perturbation formalism is effective for outgoing radiation calculations.

The method improves estimates of gravitational waves from black hole mergers.

Examples demonstrate the applicability to close-limit black hole scenarios.

Abstract

The perturbation theory of black holes has been useful recently for providing estimates of gravitational radiation from 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 present the second order formalism for perturbations of Schwarzschild spacetimes. The emphasis is on practical methods for carrying out second order computations of outgoing radiation. General issues are illustrated throughout with examples from ``close-limit'' results, perturbation calculations in which black holes start from small separation.