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We describe the hyperboloidal compactification for Teukolsky equations inKerr spacetime. We include null infinity on the numerical grid by attaching ahyperboloidal layer to a compact domain surrounding the rotating black hole andthe orbit of an inspiralling point particle. This technique allows us to study,for the first time, gravitational waveforms from large- and extreme-mass-ratioinspirals in Kerr spacetime extracted at null infinity. Tests and comparisonsof our results with previous calculations establish the accuracy and efficiencyof the hyperboloidal layer method.

Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime