Comment by scotty79

12 hours ago

Hi. Sorry to bother you here. Could you point out what error am I making in my, I believe, very simple objection?

https://news.ycombinator.com/threads?id=scotty79&next=441240...

4 comments

scotty79

tl;dr The farrrr-from-the-horizon part of Schwarzschild spacetime is just not like our spacetime. 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.

Schwarzschild infinity is unphysical, while your notion of t(Earth) is physical because we can associate a worldline with the planet's centre of mass (COM), hold the COM at the spatial origin of a system of spacetime coordinates, and use whatever "timestamps" we like on the time axis. 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; if we count of seconds before or after t(Earth)=infinity, we still have t'(Earth)=infinity, so it's not a very good choice of coordinate.

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. The root of your problem seems to be mis-identifying the local time at Earth with the Schwarzschild time at infinity in the Schwarzschild solution. We aren't at infinity to any known black hole: between us and the most distant black holes we know of is expanding spacetime not found in Schwarzschild's solution; betwee us and the nearest black holes is substantially and lumpily curved spacetime and plenty of matter unlike Schwarzschild's unique pointlike mass surrounded by non-lumpy matterless vacuum; none of the astrophysical black holes are infinitely old today (whereas Schwarzchild black holes are infinitely old at every time, otherwise the spacetime would not be static); and in general exact solutions of the Einstein Field Equations -- even ones that are not eternal -- do not superpose cleanly with solutions for other black holes (and crucially there are no black hole mergers in Schwarzschild), ordinary stars, galaxies, clusters, and expanding spacetime. As an example: 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? What do you make of the evolution of mass of the stellar black hole, from your vantage point hugging an SMBH's horizon?

Short of taking a series of courses or finding an informal short-term tutor to walk you through particular things (you can find either at your local tertiary education school, like a community college or university), there are plenty of good textbooks on General Relativity. You seem to have found Wald's, which is probably the most rigorously and densely mathematical of several popular teaching choices, and it does not seem to have helped you. I'd guess you'd be better off with e.g. Carroll's Spacetime and Geometry or Wheeler's Gravity and Spacetime.

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. We can then trace light rays from e.g. a quasar, across early expanding space to a SMBH or elliptical galaxy acting as a gravitational lens, and then across later expanding space to an approximation of our neighbourhood, adapting the rays at each shell boundary. Although there is very definitely a subregion of black hole solution in that kind of approach, the asymptotically flat part of Schwarzschild is cut away along with its distant infinities. One can compare this cutting and pasting to the Hill sphere of influence of Jupiter and those of its satellites, for example, if one were interested in a navigational plan like Juno's or JUICE's.

scotty79 3 hours ago
> 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.
- raattgift 1 hour ago
  
  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.