Determine the zero-frequency electromagnetic and charge-dependent nonlinear memory

Determine the zero-frequency, or direct-current, memory contributions to the gravitational waveform of electrically charged black-hole binaries, including the charge-dependent corrections to the standard nonlinear memory, and treat their secular accumulation consistently on the radiation-reaction timescale.

Background

The paper derives oscillatory electromagnetic-memory contributions to the gravitational radiative multipole moments at 2PN accuracy, but the harmonic decomposition used for the circular-orbit calculation does not capture zero-frequency components. These direct-current pieces can accumulate secularly over the radiation-reaction timescale rather than remaining ordinary oscillatory corrections.

The authors also note that a complete treatment must combine the electromagnetic DC terms with charge-dependent corrections to the standard nonlinear memory present for neutral binaries. Although those corrections formally begin at higher PN order, their secular accumulation can make them leading-order relevant for the memory signal.

References

The zero-frequency pieces, which give rise to the so-called direct-current (DC) memory, are not included in the present analysis and will be addressed in future work.

— Charged black-hole binary radiation at second post-Newtonian order  (2609.02825 - Placidi et al., 2 Sep 2026) in Section 5, subsection “Memory contributions”; reiterated in Section 8, “Conclusion”