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I present a new general formalism to characterize the accuracy of future tests of general relativity performed with gravitational-wave observations. The formalism handles in a unified manner the tests based on measuring the coupling coefficients of well-defined alternative theories (such as Brans–Dicke gravity), the tests based on quasi-phenomenological extensions of waveform families (such as the parametrized post-Einstein formalism), and the tests based on treating the post-Newtonian phasing coefficients as independent quantities. Using the formalism, I characterize prospects for upcoming experiments, and show, for instance, that advanced interferometers will at best show that general relativity is unmodified at the 1–10% level. Last, I argue that the greatest challenge will be controlling the systematic effects due to instrument and waveform-model inaccuracies.
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