[scotty79]

> It only has to happen at one place in the spacetime, namely at the horizon itself.

In theory yes. In practice if you can't point to a single moment and place in the concievable past and future history of human race that is simultaneous (in any practical sense) with this point in spacetime on the event horizon then from practical perspective it will never happen.

> one obtains the free-faller's geodesic by solving the EFEs in the block spacetime, and one notes that some of that geodesic is outside the black hole, some of it is inside the black hole, and that portion inside the black hole at no point in the future exits the black hole

This isn't that much different than plotting geodesic of a rock thrown in Earth's gravity and noticing that at some point it crosses the surface of the Earth and goes under. Except in GR the math itself provides the reason why the part below event horizon should be outside of our consideration.

We just chose to disreagrd it by carefully picking coordinate system so that infinities don't spoil our fun and we can seemlessly cross from physics to philosophy.

[raattgift]

The practical sense is the binary-merger waveforms detected at LIGO, Virgo, and Kagra, which were emitted in the detectors' (and humanity's) past lightcones. We don't even have to consider "the ... future history of human race"; the gravitational-wave ringdown is from after the two horizons touched (and in particular the intermediate stage of the ringdown encodes the crossing of light from the light or photon ring structure around the not-yet-merged black holes into the final merged object, and the recapture of quite a lot of gravitational radiation scattered in the strong-gravity zone around the not-quite-in-contact binary).

> Except in GR the math itself provides the reason why the part below the event horizon should be outside of our consideration

No it doesn't, and this has been known about since the 1920s (and reasonably understood since 1939 and well-understood since the early 1970s), and you can find out about this in any GR textbook, for example §12.2 of Wald, and problems 1 and 4 at the end of chapter 12. You should try solving those two exercises like any grad student (being sure to read problem 4 and to think about why it's asking for an upper limit) before making the sort of wrong claim about "the math itself" you made above.

A couple of things to understand: (1) in general black hole solutions do not superpose linearly [this is the thrust of problem 4]; (2) there are multiple lines of evidence supporting black hole mergers; (3) gravitational radiation is generic to any quasicircular orbit (not just black holes), with the emitted frequency and amplitude inversely proportional to the orbital diameter; (4) frequencies and amplitudes for some detections (e.g. GW150914) are too high for solid self-gravitating bodies anywhere in the sky.

You can't put a rock in a 100-millisecond orbit around the Earth; LIGO has ample data in the ~ 30 - 7000 Hz range. The gravitational wave ringdown of a neutron-star/neutron-star, neutron-star/black-hole, or black-hole/black-hole merger is totally unlike what one gets from a rock hitting the Earth.

The curves of rocks thrown in Earth's gravity don't become incomplete just because they transition from free-fall (geodesic motion) to accelerated (while resting on the surface). One can literally lift bits of meteorite out of craters. There's enough cosmic dust <https://en.wikipedia.org/wiki/Cosmic_dust> around launch sites that it's inevitable that some bits of meteorite have been taken back to space and are now in free-fall somewhere in or near the solar system (or as another possible example, some of the nickel or iridium in Voyager 1 components, if the ore was mined in Sudbury, Canada).

The curve of every part of a rock chucked through a black hole horizon ends inside the horizon. That curve-confinement is the characteristic feature of a black hole in General Relativity: no trapping surface, no black hole (Wald again, proposition 12.2.3). Where there is a trapping surface,no known high-energy behaviour of matter avoids collapsing gravitationally into a configuration in which every (non-spacelike) curve of the matter inside the horizon ends up becoming future-inextendible (that's what the singularity does: any curve touching it cannot be extended further within the horizon).

> coordinate system so that infinities don't spoil our fun

Curvature scalars don't diverge just below the horizon of even a stellar-mass black hole. Coordinate divergence is not the same as curvature divergence, and different systems of coordinates on a single arrangement of mass can diverge at arbitrary radial distances, including very very large ones.

> physics to philosophy

"Does the ringdown overtone of a merger of two black holes encode any of the accretion history of each black hole?" is a physical rather than philosophical question and is an avenue for testing solutions of the Einstein Field Equations (including approximate ones solved numerically) against astrophysical data. See for example https://www.ru.nl/en/research/research-news/the-observation-...

[scotty79]

> for example §12.2 of Wald, and problems 1 and 4 at the end of chapter 12

Literally the first paragraph of problem 1 states my exact objection.

"Since an observer outside a black hole does not lie within the causal future of the black hole, such an observal literally cannot "see" the black hole. As is apparent from Figure 6. 1 1 , an observer looking at a region where gravitational collapse has occurred would, in principle, see the collapsing matter at a stage where it is just outside the black hole."

What I can't understand is how people can smoothly ignore it and calculate something that is going to happen after infinite time passes on Earth. Because those things will literally never exist, because there's simply not enough time anywhere in the universe outside of any event horizon. For the points on event horizon there's no causality line that crosses our future and there's no simultaneity line (however you define it) that crosses our future. It just won't happen, ever, in any practical sense.

> The practical sense is the binary-merger waveforms detected at LIGO, Virgo, and Kagra, which were emitted in the detectors' (and humanity's) past lightcones.

Aren't those waveforms just in agreement of theoretical prediction of what happens as the matter approaches event horizon? Because we can't have any information about it crossing it. I don't have a problem with that part. I have a problem with the part that's theorized to happen after those signals get stretched, red-shifted and stopped by gravitational dilation.

> The curve of every part of a rock chucked through a black hole horizon ends inside the horizon.

Sure at t(Earth)=infintiy.

> Coordinate divergence is not the same as curvature divergence, and different systems of coordinates on a single arrangement of mass can diverge at arbitrary radial distances, including very very large ones.

Curvature is not the only real thing. Time, which is a coordinate is also a very real thing and when it diverges to infinity at any finite point for any observer, we can't just sweep it under the rug with a coordinate change.

> "Does the ringdown overtone of a merger of two black holes encode any of the accretion history of each black hole?" is a physical rather than philosophical question and is an avenue for testing solutions of the Einstein Field Equations (including approximate ones solved numerically) against astrophysical data.

I have absolutely no problem with that. What I have problem with is postulating that anything happens (from our point of view) in that observed region of space after the ringdown overtone of a merger happens. In my opinion when the signals get too faint and redshifted for us too observe nothing ever happens there, because time there physically nearly stops for us.