As for what it is made of, that is one of the great open questions in theoretical physics right now, but also possibly where the analogy breaks down. Because of Lorentz Invariance (light travels at the same speed in all reference frames), it is hard to suppose that there is such a thing as "atoms of spacetime" from which it is made. However, because our world is cosmological and the big bang does actually pick out a preferred reference frame, Lorentz Invarience has to be approximate in some way.
Because of cosmology and the breakdown of reductionism at plank scales, it seems that the notion of spacetime itself is approximate and needs to be replaced with something else. Some people are trying to derive spacetime from purely quantum mechanical notions, while other people are trying to find dual systems where spacetime and quantum mechanics emerge hand-in-hand. The two approaches I'm familiar involve either holography or purely geometric and combinatorial ideas where the principles of general relativity and quantum mechanics are outputs rather than assumptions.
https://www.youtube.com/watch?v=WECVq2YBduY&t=0s&index=9&lis...
A particular solution to a set of equations does not usually have all the symmetry of the equations. In fact, I would say that, any solution to GR equations with energy and/or matter (assuming homogeneity on large enough scale) you will find something that looks like a preferred frame of reference.
After watching, I have a question, please forgive if it is ridiculous or displays some fundamental problem with my layman's understanding of the subject.
If time becomes space-like, and space becomes time-like, can we think of black holes as "time stars"? Would every black hole within our observable universe contain information from all light cones within the observable universe? In other words, would different black holes contain different information?
Does my question make sense?
However, as for black holes containing the same information, our universe is expanding uniformly at an accelerating rate, and this results in cosmological horizons beyond which objects are moving faster than the speed of light (with respect to the frame of reference). Therefore, black holes in different galaxies shouldn't be able to have access to the same light cones without compromising the principle of locality. Although, if you believe that entangled black holes in different galaxies would lead to the same singularity ("ER=EPR" [1][2]), this becomes more complicated and is way out of my depth.
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Nima Arkani Hamed | Unification and Fundamental Phyics: A Status Report 9-21-2018
[0]: https://www.youtube.com/watch?v=pXYvFMqwbhc
Leonard Susskind Public Lecture | "ER = EPR" or "What's Behind the Horizons of Black Holes?"
[1]: part 1: https://www.youtube.com/watch?v=OBPpRqxY8Uw
[2]: part 2: https://www.youtube.com/watch?v=uiG_EtVQu5o
One point that was made in the video was that inside a black hole, space is collapsing faster than light. This seems like more than a change to coordinate system? Doesn't this mean that time is also moving faster than light? Could time effectively become "solid" at the singularity, with all events within the black hole's light cone at a single point in time, but in infinite space(ignoring Hawking Radiation)?
No, this refers to the fact that inside a black hole you can travel as fast as you want and do whatever you want but even if you move around at the speed of light, you still won't be able to escape the singularity. This is because the singularity is a so-called timelike singularity – it lies in your future. It's not a point in space somewhere that you can walk around and poke; while you're in the black hole, it's actually completely invisible to you until you hit it. You can basically compare the singularity to your own death: While you can't see it right here and right now but you know for sure that you'll reach it at some point in your future.
A physicsy way of saying all this is that, inside the black hole, all future-directed worldlines emanating from a given spacelike surface will converge and eventually hit the singularity. (This is what Nima Arkani-Hamed means when he says that space "collapses".) Another way of saying this is that the aforementioned surface is a so-called trapped surface.
Back to a more intuitive explanation: In a way, falling into a black hole and towards the singularity is like falling down a waterfall: Once you've stepped over the edge (crossed the event horizon), you certainly won't be able to stop yourself from falling anymore. You cannot fall up and escape gravity.
Here's a website which explains this way of looking at black holes as "waterfalls" of space a bit further: https://jila.colorado.edu/~ajsh/insidebh/waterfall.html
> Doesn't this mean that time is also moving faster than light?
As mentioned in my other comment, I recommend steering clear of the terms "time" and "space" as those are not individually well-defined and equally agreed upon by all observers. Instead, time and space are relative – if I use a different coordinate system than you, we will have very different notions of which events occur at the same point in time (and are thus part of the same spatial slice). It's called relativity for a reason. :)
So, my counter question to your question would be:
> Time as measured by whom? ;)
But even if you define time with respect to a given observer, it still does not "move" or have a "velocity" that you could compare to the speed of light. Only massive objects actually move through spacetime and only when they're close enough, you can compare their relative velocities.
> If time becomes space-like, and space becomes time-like, can we think of black holes as "time stars"?
doesn't make much sense to me. Time does not become spacelike nor does space become timelike. In General Relativity, time and space are not individually defined in an observer-independent fashion in the first place. The terms we use instead are "timelike directions" and "spacelike directions" as well as timelike / spacelike hypersurfaces because they are defined in such a way that all observers will agree on whether a direction / hypersurface is timelike / spacelike. So now that we've replaced the terms "time" and "space" with "timelike" and "spacelike", I hope you'll see that your question is not exactly well-defined.
But maybe I'm misunderstanding you, so please feel free to elaborate on your questions. (Or to point me to an explanation from the video in case you're referring to one.)
As for your second question:
> Would every black hole within our observable universe contain information from all light cones within the observable universe? In other words, would different black holes contain different information?
I'm afraid I can't follow this question, either. Would you mind rephrasing it? My initial impression is that you might have a wrong idea of what a lightclone is.
What they mean when saying that "time and space switch roles inside a black hole" is that in standard Schwarzschild coordinates, the direction given by the time coordinate becomes spacelike at the event horizon and, likewise, the radial coordinate becomes timelike. This statement is specific to Schwarzschild coordinates, though, or, more generally, any coordinate system that is singular/ill-defined at the event horizon. There are coordinate systems, however, that don't exhibit this pathological behavior at the horizon and, there, no switching occurs.
There were similar objections to the existence of the electromagnetic field, back in the 1890s. But it turns out that fields can propagate energy independent of any non-field objects in them... and if it can carry energy, then how can you say they aren't real?
Spacetime carries energy in the form of gravitational waves. So it is as much an object as anything else that carries energy, whether it be in wave form or mass form.
* Unless you happen to be a photon.