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Asymmetric emission of gravitational waves during a compact binarycoalescence results in the loss of linear momentum and a corresponding `kick'or recoil on the binary's center of mass. This leads to a direction-dependentDoppler shift of the ringdown gravitational waveform. We quantify themeasurability of the kick imparted to the remnant black hole in a binary blackhole merger. Future ground- and space-based gravitational wave detectors willmeasure this effect to within $\sim 2\%$ to $\sim 30\%$ for a subset of theirexpected observed sources. Certain binary configurations in the LISA band mayallow a sub-percent-level measurement of this effect. This direct measurementof black hole kicks can also facilitate a novel test of general relativitybased on linear momentum balance. We formulate this kick consistency test viameasurement of a null variable that quantifies the difference between theinferred kick (using numerical relativity) and that observed via theDoppler-shifted ringdown signal. This null variable can be constrained (at 90%confidence) to $\sim 10\%$ to $30\%$ with Cosmic Explorer and to $\sim 3\%$ to$12\%$ with LISA.

Testing general relativity via direct measurement of black hole kicks