Gravitational-wave interferometers are expected to monitor the last threeminutes of inspiral and final coalescence of neutron star and black holebinaries at distances approaching cosmological, where the event rate may bemany per year. Because the binary's accumulated orbital phase can be measuredto a fractional accuracy $\ll 10^{-3}$ and relativistic effects are large, thewaveforms will be far more complex, carry more information, and be far harderto model theoretically than has been expected. Theorists must begin now to laya foundation for extracting the waves' information.
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