Perturbation theory of black holes: Generation and properties of gravitational waves Available to Purchase

The aim of these notes is to give a solid basis on the theory of gravitational waves generation using the black hole perturbation description. We present an analytical and numerical point of view. In these notes we present the derivation of the Newman-Penrose equations by means of the null tetrad formalism, with particular attention to the derivation of the scalar functionwhich will describe the gravitational wave, i.e, Ψ₄. Next, we describe the case of a Schwarzschild background and show with great detail how to express the evolution equation in a way that can be dealt with in a numerical fashion. We show how to obtain the profiles of the gravitational waves and explain how to analyze several of their properties.