Distortion of gravitational-wave packets due to their self-gravity

When a source emits a gravity-wave (GW) pulse over a short period of time, the leading edge of the GW signal is redshifted more than the inner boundary of the pulse. The GW pulse is distorted by the gravitational effect of the self-energy residing in between these shells. We illustrate this distortion for GW pulses from the final plunge of black hole binaries, leading to the evolution of the GW profile as a function of the radial distance from the source. The distortion depends on the total GW energy released γ and the duration of the emission τ, scaled by the total binary mass M. The effect should be relevant in finite box simulations where the waveforms are extracted within a radius of ≲10²M. For characteristic emission parameters at the final plunge between binary black holes of arbitrary spins, this effect could distort the simulated GW templates for LIGO and LISA by a fraction of 10^-3. Accounting for the wave distortion would significantly decrease the waveform extraction errors in numerical simulations.