This paper studies a surprising geometric feature that appears when two black holes collide head-on. Using numerical simulations of two non-spinning black holes, the authors track the black hole boundaries and show how sharp points, or cusps, form on otherwise smooth horizons. They measure how the mass and higher mass multipole moments behave at these cusps and propose a simple, phenomenological model for the process.

Instead of relying only on the outgoing gravitational waves, the team follows quasi-local horizons—three-dimensional surfaces built from a sequence of two-dimensional “marginally outer trapped surfaces” (MOTSs). These quasi-local horizons (QLHs) can be evolved in time inside the simulation. The authors compute horizon measures such as mass and higher multipoles as functions of time up to and through the merger. They report a discontinuous jump in those quantities at the moment of merger, and they connect that jump to the formation of a cusp on the merging horizons.

At a high level, the idea is that horizons change when infalling radiation and nonlinear curvature fall onto them. QLHs record those fluxes directly, so their area and multipole moments change. In a head-on merger the two separate horizons approach each other and then connect through a cusp. That cusp is a singular geometric feature in the otherwise smooth horizon foliation and plays a central role in how the two initial black holes become one remnant.

This horizon-based view offers a complementary route to the more common waveform-based methods for predicting the remnant’s properties. If the link between horizon dynamics and the outgoing gravitational waves is robust, then tracking QLHs could help predict which quasi-normal modes (the characteristic “ringing” frequencies of the remnant) are excited and with what amplitudes. The paper cites growing numerical evidence that infalling fluxes at the horizon and the observed wave signal are closely related, so horizons may contain useful, local information about the merger.