Accurate time--domain gravitational waveforms for extreme-mass-ratio binaries

The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation is improved significantly. Comparing energy fluxes in gravitational waves with highly accurate frequency-domain results for circular equatorial orbits in Schwarzschild and Kerr, we find agreement to within 1\% or better, which may be even further improved. This improvement is with respect to previously reported deviations of 10--20\% in the energy flux. We apply our method to orbits for which frequency-domain calculations have a relative disadvantage (namely, summation over very many modes would be required), specifically high-eccentricity (elliptical and parabolic) ``zoom--whirl" orbits, and find the energy fluxes, waveforms, and characteristic strain in gravitational waves. Our calculations maintain the desired accuracy also for orbits in the strong field regime. This proof-of-concept work demonstrates that time-domain generation of waveforms can be accurate and computationally efficient, and can complement frequency-domain calculations where the latter have relative disadvantages, in addition to providing an independent check on them. Further improvements in particle modeling, non-uniform grids (including adaptive mesh refinement), and parallel computation, in addition to grid refinement and enlargement of the computational domain, may improve the accuracy even further.