by scotty79 | 2025-06-16 20:42:18+00:00
> Only near and outside the horizon (or better, in the absence of a horizon) does Schwarzschild become a decent physical approximation for anything in our universe.

I guess that's my point. Noting at or inside event horizon (of any kind, not just Schwarzschild solution) is physical. It's pure math, no matter how fun, has nothing to do with reality.

> But we could decide that t(Earth)=infinity could be yesterday, or tomorrow, or a billion years ago, or a couple billion years from now;

No, we cannot. Because as you stated t(Earth), by which I meant time as it passes on Earth, is physical... Now I think I should write t_Earth instead so it looks more like subscript not function application. So t_Earth = Infinity is the moment after all of the time already passed. After every finite moment already occurred. So t_Earth = Infinity doesn't really exist ever. It's purely mathematical concept. Abstract limit of the real thing.

> I think you have a misunderstanding that is probably beyond my ability to help you with, since we can't do interactive blackboard work in HN comments.

That's probably true. Even a blackboard wouldn't help because you seem to be interested mostly in minutia and specifics while my problem lies with general reality (pun intended) of all of this and which part is real and which is just extrapolation to times that don't exist and why physicists usually don't seem to care to differentiate between one part and the other.

> We aren't at infinity to any known black hole

I'm saying exactly opposite. The black hole (its event horizon to be precise) is at infinity (infinite time) to us. Any infalling object at Kruskal diagram crosses the line clearly labeled as t=infinity which in reality can't happen because there's simply isn't infinite amount of time in the universe.

> none of the astrophysical black holes are infinitely old today

To be honest that's another claim I just don't take on faith, especially in the light of the discovery of early developed galaxies and the fact that galaxies developing this early this fast would emit so much light that it would contribute to CMB (even up to 100% of it) which throws off all of our precise math theories of how everything started. I'm more inclined to believe that every astrophysical black hole existed at the the time when CMB was emitted (and before) and had exactly same size (of the event horizon) as it has today.

> and crucially there are no black hole mergers in Schwarzschild

Do you say that because they are mathematically impossible (which I would agree with) or just because Schwarzschild modeled just one black hole so there's nothing to merge with?

> hover just above the apparent horizon of Sagittarius A*. Look at a stellar black hole in our galaxy. What do you make of infallers plunging towards the smaller black hole?

Let's assume your trajectories are parallel to skip issues of special relativity. If he's closer to his event horizon than you are he's slowed down in time for you as he is for the rest of the universe outside (just slightly less). If he's farther away he lives at a pace accelerated relative to you, in the same manner that the outside world is accelerated for you. The specific math of how both of you tend to infinite time dilationas you approach your respective event horizons should show if relative time dilation between you tends to some ratio (or 1) or infinity. I don't know which is the case.

> There is also the Israel-Darmois thin shell method, which is technically annoying but lets us cut the central part of an e.g. Schwarzschild solution and paste it into a cosmology populated with other such pasted-in subregions.

I'm not that interested in pasting them statically far away. 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. Maybe (|)

Thanks for recommendations for further reading.