Researchers have derived the gravitational-wave signal that two nonspinning compact objects emit when they scatter past each other, in the extreme-mass-ratio limit where one body is much lighter than the other. The new result gives the waveform directly as a function of time, rather than as a function of frequency. It is accurate through the fifth post-Minkowskian order (an expansion in powers of Newton’s constant) and through seventh post-Newtonian order (an expansion in powers of velocity), and is valid to first order in the small mass ratio.

To get this result the authors used perturbative methods that treat the light body as moving on the fixed background of the heavy body, with first-order corrections from the small body’s own gravity. This is the first-order self-force approximation. The calculation produces the time-dependent multipolar radiation—the detailed pattern of gravitational waves in time—during the short burst of radiation that comes from the close passage. The waveform includes effects that depend on the system’s past history, such as nonlinear “memory” contributions, because the time-domain approach carries those hereditary pieces directly into the signal.

A time-domain waveform is useful because a scattering encounter is strongly non-adiabatic: the orbital frequency and acceleration change rapidly near closest approach, and the radiation is concentrated near that time. Time-domain formulas let one follow the orbital motion, radiation-reaction effects, and multipolar structure together as they evolve. This complements earlier first-order self-force work that has mostly given results in the frequency domain, and so helps bridge time- and frequency-domain descriptions of the same physical radiation.

The authors have already checked parts of the calculation against other observables. In prior work they used the waveform to compute the energy and angular-momentum carried away by the waves, finding radiative losses at the 5PM and 4PM levels (with the same post-Newtonian accuracy) that agree with recent amplitude-based calculations. That agreement gives confidence in this time-domain construction and means the waveform can serve as a benchmark for future methods.