The stellar graveyard

This chapter introduces the different classes of compact objects—white dwarfs, neutron stars, and black holes—that are relevant for gravitational-wave astronomy. The ideas are placed in the context of developing an understanding of the likely endpoint(s) of stellar evolution. Key ideas like Fermi gases and the Chandrasekhar mass are discussed, as is the emergence of general relativity as a cornerstone of astrophysics in the 1950s. Issues associated with different formation channels for, in particular, black holes are considered. The chapter ends with a discussion of the supermassive black holes that are found at the centre of galaxies.

Gravitational waves

This chapter introduces the notion of gravitational waves, starting with a discussion of weak fluctuations on a flat spacetime background and later extending the notion to a general curved spacetime. The effect the waves have on matter is described and the derivation of the quadrupole formula, which allows estimates of the strength of relevant sources, is outlined. The vexing issue of the energy carried by gravitational waves is also discussed.

A brief survey of general relativity

This chapter provides an overview of Einstein’s geometric theory of gravity – general relativity. It introduces the mathematics required to model the motion of objects in a curved spacetime and provides an intuitive derivation of Einstein’s field equations.

Opening the window

This chapter provides a brief survey of gravitational-wave astronomy, including the recent recent breakthrough detection. It sets the stage for the rest of the book via simple back-of-the-envelope estimates for different sets of sources. The chapter also describes the first detection of a black hole merger (GW150914) as well as the first observed neutron star binary event (GW170817) and introduces some of the ideas required to understand these breakthroughs.

Anatomy of a merger

This chapter discusses the different stages of an inspiralling neutron star binary system, through the formation of a black hole and the possible emergence of a gamma-ray burst. Tidal effects and the information encoded in the so-called Love numbers are explored. The violent dynamics of the merger is considered and models of gamma-ray bursts and the late time kilonova emission are also explored.

From oscillations to instabilities

This chapter discusses seismology aspects of, in particular, neutron stars. The fundamental mode and the pressure and gravity modes are introduced by simple examples, as are the inertial r-modes of a rotating star. A discussion of uniform density ellipsoids leads on to the notion of the gravitational-wave-driven Chabdrasekhar–Friedman–Schutz instability.

Binary inspiral

This chapter provides a simple application of the quadrupole formula to the relevant setting of binary inspiral. The results are compared to the celebrated observations of the Binary Pulsar PSR1913+16, demonstrating the need to account for orbital eccentricity.

From black holes to stars and the Universe at large

This chapter discusses relevant solutions to Einstein’s field equations, describing black holes, neuotrn stars, and the evolution of the Universe. It provides a brief introduction to relativistic fluid dynamics, including an exploration of the weak-field (Newtonian) limit.

Colliding black holes

The standard approaches to numerical simulations in general relativity are introduced, starting with the 3+1 formalism. General computational issues are discussed and the problem of providing relevant initial data for simulations is touched upon. Different slicing conditions and the extraction of wave from a numerical simualtions are discussed. The developments through to successful simulations of merging black holes are surveyed.

Black-hole dynamics

The main ideas from black-hole perturbation theory are introduced, starting with stability isses and leading on to the notion of quasinormal modes. The motion of test bodies is considered, making it possible to estimate the gravitational waves emitted in a black-hole merger, and issues associated with the self-force problem are considered.