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The detection of gravitational waves from extreme-mass-ratio inspirals withupcoming space-borne detectors will allow for unprecedented tests of generalrelativity in the strong-field regime. Aside from assessing whether black holesare unequivocally described by the Kerr metric, such detections may placeconstraints on the degree of spacetime symmetry. In particular, depending onexactly how a hypothetical departure from the Kerr metric manifests, the Cartersymmetry, which implies the integrability of the geodesic equations, may bebroken. Here, we examine the gravitational waveforms associated withnon-integrable extreme-mass-ratio inspirals involving a small-mass companionand a supermassive compact object of general relativity, namely theManko-Novikov spacetime. We show that the waveforms displays sudden frequencyjumps, when the companion transverses resonant islands. These findingsdemonstrate that such abrupt manifestations in the gravitational-wavefrequencies are generic, have a genuine astrophysical origin and function as adistinctive signature of chaotic phenomena in extreme-mass-ratio binaries.

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals