The art and science of black hole mergers

The merger of two black holes is one of the most extraordinary events in the natural world. Made of pure gravity, the holes combine to form a single hole, emitting a strong burst of gravitational radiation. Ground-based detectors are currently searching for such bursts from holes formed in the evolution of binary stars, and indeed the very first gravitational wave event detected may well be a black-hole merger. The spacebased LISA detector is being designed to search for such bursts from merging massive black holes in the centers of galaxies, events that would emit many thousands of solar masses of pure gravitational wave energy over a period of only a few minutes. To assist gravitational wave astronomers in their searches, and to be in a position to understand the details of what they see, numerical relativists are performing supercomputer simulations of these events. I review here the state of the art of these simulations, what we have learned from them so far, and what challenges remain before we have a full prediction of the waveforms to be expected from these events. 1 Black-hole coalescence systems Black holes are the ultimate in strong gravity, and the details of their merging require general relativity for any kind of even approximate description. Nevertheless, it is one of the remarkable consequences of general relativity that, during the orbital phase before coalescence, the black holes follow orbits that are described to first order by Newtonian gravity: their interaction when separated by a significant distance does not reflect the enormously strong gravity inside and near them. Only when they come within a few tens of gravitational radii do we require full general relativity to describe the dynamics. Before that, the post-Newtonian approximation – an asymptotic approximation to general relativity valid for small orbital velocity (v/c ≪ 1) in gravitationally bound systems – provides a systematic approach to studying the orbital inspiral phase, where orbits shrink and lose eccentricity through the radiation of energy and angular momentum in gravitational waves.[1] The classic test of gravitational wave theory, the Hulse-Taylor binary neutron-star system, is very accurately described by such an approximation.[2] The gravitational radiation emitted by orbiting black holes comes out at multiples of the orbital frequency forb, starting at fgw = 2forb. Higher harmonics are important only if the orbit is highly eccentric. Other frequencies, including forb itself, can appear in the spectrum from the coupling of black-hole spins to the orbital angular momentum and to each other, but this is significant only