After decades of effort, numerical relativists can now simulate the inspiral and merger of two black holes orbiting each other. That computational triumph has come none too soon—physicists are on the verge of detecting gravitational waves for the first time, and at long last they know what to look for.

Black holes are strong-field objects whose properties are governed by Einstein’s theory of gravitation—general relativity. A black hole is a region of spacetime that cannot communicate with the external universe. The boundary of that region defines the surface of the black hole, called the event horizon. Isolated black holes are remarkably simple. They are described by analytic solutions to Einstein’s equations and are uniquely parameterized by just three quantities: their mass M, spin J, and charge Q. Since charged objects in space are rapidly neutralized by the surrounding plasma, one usually assumes Q = 0 for real...

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