Comment by raattgift

Sorry, I don't want to get into metaphysics.

Black hole mergers are studied using post-Newtonian methods and numerical methods because there is no general analytical approach known. SXS, Simulating eXtreme Spacetimes, and the black hole perturbation toolkit both have web presences, you could start there. There is also an academic literature on matching the waveforms in both regimes. These are checked against results from multimessenger astronomy.

> I'd really love to see what shape two Schwarzschild blackholes (and by that I mean their event horizons because, I don't believe anything beyond them is real to us) hitting each other could look like

This is well into the numerical relativity regime.

ETA: I'd pick <https://www.youtube.com/watch?v=jkpfXByQHxA> (SXS collab, "Event horizon for equal mass inspiral BBH in two coordinate systems") and the zoom-in at <https://www.youtube.com/watch?v=p4MTsCDtHMM> from a quickie cruise through some visualizations. There are links in the video description. Do beware that there are several types of horizon involved here, and they will not match your intuitions from Schwarzschild (see the point made in the zoom-in video description) which I would wager are built on the presence of a static Killing field which becomes null at the horizon, but the entire Killing field doesn't exist in these BH merger spacetimes. Roughly, though, if anything is in an orange region, it stays in an orange region. That includes a lot of gravitational radiation moving inwards in the purple region. [ETA again: the related Phys. Rev. D paper <https://arxiv.org/abs/1606.00436> has some nice details about the "duck bill" topology, too, and offers further detail on the purple region.]

https://www.youtube.com/@mpi_grav has several videos particularly in their NR playlist <https://www.youtube.com/watch?v=acHmN2MlJQQ&list=PLSYkic-Csf...>. Look for distortions in the BH horizons (whether it's an apparent horizon or some comparable surface gets into metaphysics; apparent horizons are at least locally observable), particularly the so-called "duck bill". Bear in mind the these are data visualizations principally of the waveforms, and the choices in intensities and hues are probably not going to be aligned with your intuition.

SXS has several videos too https://www.youtube.com/@SXSCollaboration - last month there was a major catalogue reorganization by the SXS collab so it may be that some internal links and semi-recent videos have issues.

And see for example https://www.black-holes.org/2024/10/02/BBH-mergers-with-spec...

Generally such simulations allow one to trace lightlike geodesics as a local probe of the lightlike horizon surfaces.

> I don't know which is the case

Exactly. That honest self-admission must be made near the start of any research programme.