Okay, so what eventually happens to this fabric of space time? When you twist a rubber band, eventually you won’t be able to twist it anymore and it’ll break. When you twist taffy enough I assume it’ll eventually just blend back into itself and not be twisted anymore.
What happens to twisted space time? Does it twist tighter and tighter to infinity? Does it sort of blend back into itself and isn’t twisted anymore?
The state of the spacetime at any given time is indistinguishable from its state at any other given time. That state includes a phenomenon which might loosely be described as twisting, but that does not mean that anything becomes twisted. For a very rough analogy, consider a whirlpool in water: The water is always moving, but never twisted.
That really doesn’t make sense. Water drop or molecules in a whirlpool are not connected and move “independently.” Doesn’t space have a connectedness property even if it’s not continuous.
What do you mean by “connectedness”?
I’m getting a bit above my head here for a precise definition, but there are discussions in cosmology as to what is the shape of the universe. For example there was debate a dozen or so years ago it might be a dodecahedron with opposite faces connected. This would see to make sense to me only if one can say this location in space is “next to” this location in space as is true for a piece of paper. But you can tear paper so this is no longer true.
It seems to me the OP was asking in spacetime can be altered or torn in the same sense so the connections change.
I was thinking continuous when I said connected, but I’m not sure that’s the word I want if we can think of space as being quantized and therefore discrete in nature so I wanted to avoid continuous.
First, do not assume that you will ever have an intuitive understanding of this, spacetime is a 4 dimensional non-Euclidian space. Our evolutionary background did not prepare us for an intuitive understanding of this at all. Understanding this as much as we can within our mental limits also requires letting go of several concepts that we are taught as true even up and to most modern terminal science degrees. And please note that the Implications of General Relativity and spinning objects is almost completely the domain of postdoctoral research.
But if you are willing to let go of some ideas that are pretty well ingrained in both our experiences and our education system you can get the gist of it. But it will never fit in to a though model that cannot let go of the Newtonian style view of reality.
For example
A thrown baseball or the IIS are actually traveling in a straight line at a constant speed while what you feel as gravity is a fictional force that is felt as you are being accelerated away from the straightest path through spacetime. This is why an astronaut feels weightless, while we think of it as that they are always falling it is more correct to think of them as traveling in a constant speed straight line. They only appear to be rotating around earth because of our frame of reference, but the mass of the earth curves space time enough that they are actually following the geodesic.
Number two above also has implications that are extremely challenging to connect with our version of reality. If the order of events is not universal some observers past may actually be another observers future. When you involve items as massive as black holes it may even be possible for an observers timeline to loop back on itself due to the curvature of spacetime. While this effect has not been experimentally observed the math works within the framework of the einstein field equations.
What was observed in the linked article is really an observation of the Lense–Thirring effect on X-rays. The flickering was demonstrated to be a result of frame-dragging, which was also detected by the Gravity Probe B satellite. In that experiment this frame dragging was detected by watching the precession of a gyroscope as it orbited the earth. This frame-dragging also results in the earth’s rotation causing precession.
Gravity does not travel faster than the speed of light, so when you have a rotating object you will also have a form of gravitational redshift which will “twist” space time. Just as the earth effects the geometry of space time so that the IIS appears to be traveling in a circle it will also induce frame-dragging that will result in precession. This precession is not a wobble as one would observe in a top, as the earth is does not have a change in it’s angular momentum. The “twisting” of space time referenced in this which makes it appear to do so for an external observer.
It is our perception, which assumes that spacetime is flat and that time is universal that makes this seem non-sensical.
The notion of connectedness that you’re referring to is the topology of the space. “Twisting” the space does not change its topology. A space with a black hole in it will have a different topology than one without, but once the black hole is there, it’ll remain that same topology.
Can you clarify if you are talking about manifold or path topology?
The “twisting” would change measurements of distance, time, and direction in local spacetime. Various events like the merging of two black wholes would alter the properties that would in effect change the path topology. Although I would not describe any of these as “tearing”. It may be better described outside of the realm of black holes. Lets say the earth, which is transferring rotational angular momentum to increase the distance between the earth and the moon. As this distances increase and as the earth-moon system tends towards tidal lock the effects of frame dragging are reduced. This has a direct impact on reducing the Lense–Thirring effect and thus changing the path topology.