Thanks once again for a well-informed post. I do have a couple of points to add, maybe minor or irrelevant, maybe not.
I am absolutely NAP (Not a Physicist) but an alterantive perspective that occurs to me is based on the fact that in the proper time of the infalling object, it just falls right in as one might expect. But we see it as asymptotically slowing as it gets closer to the event horizon, and presumably coming to a stop there. Which is the reality? Maybe we can hypothesize that what we see as increasing slowness extrapolating to a complete stop at the horizon is just an illusion caused by the conflict between our frame of reference and the one local to the black hole. One would think that the local frame of reference is always the “true reality”.
This seems to me to be equivalent to the "space (one of the spatial dimensions) and time switch places.
Makes sense. I would not expect the observer’s watch to suddenly measure distance, of course, or the ruler to suddenly measure time. I would expect, as you say, the observer to not notice anything particularly unusual in this respect, except that the spacetime the observer was now in would be different from our own while having an equivalent geometry.
There’s a fanciful hypothesis that the entire universe might be a gigantic black hole, whatever that may really mean. Which might raise the question, so why aren’t we all falling into the singularity? To which the proper answer is, how do you know we’re not? There’s an apparently inescapable force drawing us through one dimension of spacetime. It’s called “time”.
Right, since you can’t see the singularity anyway, it’s not obvious to you where (or when, or whatever) it is. For the infalling observer, a future where a singularity is inevitable, a future with no singularity at all, and a future where you might or might not reach a singularity all look the same, since whatever the future holds, you can’t see.
The simplest such models correspond to a “Big Crunch” universe, where the universe stops expanding at some point and starts falling back in on itself. In such a model, the Big Crunch itself, the singularity at the end of time, is, in fact, the singularity at the center of the hole. Of course, such simple models are now ruled out by Dark Energy or whatever the heck we call it, and black hole models with dark energy get pretty weird.
Fascinating, thank you! The best part is that not that many years ago this stuff would have been considered crazy sci-fi speculation, but here it was detected by the gravitational wave, by an ostensibly associated gamma-ray burst, and apparently by visual evidence, too. Very cool!
When jumping from Galilean relativity to special relativity, some simplicities are lost. For instance, we lose the notion that events always have a well-defined time order. One observer might say “A happened before B” and another might say “B happened before A”, and they are both right. Both are real descriptions of the world, just according to two different observers. We can still hold on to the ideas of a global reference frame, well-behaved global coordinate systems, and spacetime slices (“foliations”) that align with somewhat clear and distinct notions of space and time. We can imagine carrying clocks and meter sticks around the spacetime to synchronize various apparatuses in order to experimentally realize this consistent global coordinate picture.
When moving from special relativity to general relativity, we have to lose a lot of that. The non-global nature of reference frames and the arbitrariness of coordinate systems come to the fore. What one observes (and how it is described in a given coordinate system) is less trivially connected to what is actually happening.
The Schwarzschild coordinate system exhibits this in a violent way. It suggests that an infalling object can never pass the event horizon. My previous post talked about how this coordinate system isn’t applicable all the way to the horizon anyway, but the separation between a coordinate system and what “really” happens is more fundamental. In this case, the poor behavior of the coordinate system can be removed by picking a different way of labeling points in the 4-dimensional spacetime. When using one of these other coordinate systems (example), a distant observer can easily describe the passage of an object through (into) the event horizon. However, they still won’t see it happen. Regardless of choice of coordinate system, they should always calculate the same observables. And indeed, even in better-behaved coordinate systems, the paths that photons can take to reach a distant observer all originate from outside the event horizon, and so the distant observer only sees photons arriving from the portion of the object’s trajectory outside the event horizon. Does that mean the object didn’t cross? No, they just can’t see it cross.
Except you can’t go backwards in time, either. The idea of what’s time and what’s space has to be defined locally. There is no unique global way to define it in GR. If you choose Schwarzschild coordinates and try to use them on the inside of the coordinate singularity, then the foliation you label t and the foliation you label r might be better relabeled. But if you choose a different coordinate system, you can dispense with both the coordinate singularity and the need to do a piece-wise swapping of what the variables mean. In that sort of coordinate system, there’s no sense in which time and space swap roles across the horizon.
Unfortunately the above link gives me: “# Error 1011 ## Access denied […]
The owner of this website (i.sstatic.net) does not allow hotlinking to that resource (/9ytEW.jpg).”
ETA: changing “https” to “http” in my browser’s address bar makes it visible, thank you Gordon_G.
Often, when sites disallow hotlinking, you get an error following the link but don’t get an error when you enter the URL into the address bar directly. The nice thing about that is, when you’re looking at the error, the URL is already in your address bar and all you need do is click on the address and hit enter. At least in browsers I know.
Worked for me in this case anyway.
Note: I’ve reported this post to the moderators in case it violates any copyright policy.
This is what I believed, except, LIGO seems to have observed gravitational wave evidence of black hole mergers. There, you have a pair of c-relative entity boundaries spiraling into contact with each other, and the wave signature progresses forward it time, eventually blooping into one big hole and ending (the wave pattern).
An object would appear to us to stop moving at the event horizon – perhaps a black hole is not quite the same thing as an object?
The conventional description is based on the assumption that the hole is much, much more massive than the infalling object, such that the black hole is not changed in any meaningful way by the added mass. That assumption breaks down badly when two objects of comparable mass are merging. A star falling into a stellar-mass black hole would cause similar problems.
I am picturing a neutron star that formed, say 6 or 8 GYa, has been wandering about the galaxy eating various dwarves in its travels and has grown to about the maximum stable size that a neutron star can get. Now it encounters a black hole freshly formed in a recent supernova, at the lowest bound for mass. In fact, the old neutron star is slightly heavier than the black hole. If it could happen, I wonder how such an encounter would play out.
The short answer is “very messily”. It’s only very recently that we even figured out how to do the calculations at all for something as simple as two black holes merging: Before a couple of decades ago, it wasn’t even possible to model it on supercomputers (by which I mean actually “not possible”, not even “possible but impractically slow”: The models just wouldn’t work at all). Introduce matter, and matter for which we still don’t even know the equation of state, and any calculation is hopeless.
But to the point of this thread, yes, matter would absolutely most definitely end up inside the hole. It’s like the old immigration quip, “We didn’t cross the border, the border crossed us”. Even if, to an external observer, the infalling matter would never cross the event horizon, the event horizon would expand out to encompass the infalling matter.
