Relate remnant DHS multipoles to progenitors

Derive explicit relations connecting the multipole moments and other invariant properties of the remnant dynamical horizon segment to those of the two progenitor dynamical horizon segments, establishing continuous links through the merger.

Background

Numerical evolutions show that progenitor DHSs evolve continuously and merge into the common DHS of the remnant, with inner horizon segments exhibiting intricate bifurcations and self-intersections. These complexities obscure direct comparisons of invariant quantities such as multipoles.

A relation between progenitor and remnant multipoles would bridge inspiral and ringdown regimes quasi-locally and reduce reliance on waveform matching, offering deeper insight into strong-field dynamics.

References

Open Issue 8 (OI-8) Can we relate the multipole moments (and other properties) of the remnant DHS with those of the two progenitor DHSs?

— Quasi-Local Black Hole Horizons: Recent Advances  (2502.11825 - Ashtekar et al., 17 Feb 2025) in Section 4.3

Resolving this field into the normal components of rigid coordinate translation and rotation would provide quantities to compare with independently measured recoil and angular momentum. We leave this decomposition and comparison to future work.

— Universal Structure of Horizon Formation in Generic Binary Black Hole Mergers  (2609.11819 - Xie et al., 10 Sep 2026) in Section Discussion and outlook, paragraph beginning “The branch expansion, Eq.~\eqref{eq:Hexpansion}, splits the birth into two fields with distinct physics.”