We describe the hyperboloidal compactification for Teukolsky equations in
Kerr spacetime. We include null infinity on the numerical grid by attaching a
hyperboloidal layer to a compact domain surrounding the rotating black hole and
the orbit of an inspiralling point particle. This technique allows us to study,
for the first time, gravitational waveforms from large- and extreme-mass-ratio
inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons
of our results with previous calculations establish the accuracy and efficiency
of the hyperboloidal layer method.Comment: 14 pages, 7 figure