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I'm quite familiar with the fabric of space time theory and as I've been quite lonely these past few weeks, I started thinking that since the universe is expanding and since the "fabric" is the universe, would our nice little sheet eventually rip and mess up space time?

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There is no "fabric" to rip.

Spacetime can stretch as much as you want (and in ways you cannot visualize - hence we use mathematics). There is no way to do anything more than distort spacetime. It can (at least in theory) be distorted is very odd ways (odd in terms of human experience) but there is no distortion that would "rip" or "tear" it. It is always there.

Regarding the expansion of the universe, think about it like a having two points some fixed distance apart. As the universe expands they become further and further apart, but it's not them moving, it's the scale factor of spacetime getting larger. The universe gets larger because the scale factor increases. In the past it was smaller and things were closer together.

There is a theoretical idea called "The Big Rip", but basically this just says that eventually the scale factor (which in this model keeps increasing) gets so large that everything is isolated from everything else, down to the level of elementary particles. But spacetime itself does not rip - it's still intact, it's just that the scale factor has become huge.

There are models of the expansion of the universe that say the opposite - that eventually the expansion stops and the scale factor stops increasing and starts decreasing and we end up with everything in a Big Crunch. Again no spacetime was hurt in the making of this model. :-)

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  • $\begingroup$ Thank you! but is it possible to destroy it or remove it? i mean, black holes do just stretch space time down to a place where nothing will ever see the light of day again. $\endgroup$
    – Leo Pan
    May 28 '20 at 3:39
  • $\begingroup$ or does the black hole simply stretch the fabric down without taking fabric from around it? $\endgroup$
    – Leo Pan
    May 28 '20 at 16:33
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    $\begingroup$ Both the big rip and big crunch most definitely "hurt" spacetime. In the big rip the Hubble parameter becomes infinitely large in a finite time. There is a definite end to the universe. The same with the big crunch. $\endgroup$
    – ProfRob
    May 28 '20 at 18:45
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What happens to spacetime as the universe expands depends very much on what is driving the expansion.

Under the normal assumption of a cosmological constant - one in which the energy density of the vacuum does not change and where the pressure is equal to minus the energy density - then the expansion becomes exponential with a Hubble parameter tending towards a constant value. i.e. $$ a \propto \exp[H t]$$ and the velocity of the expansion $$ \dot{a} \propto H \exp[Ht] = Ha$$

In such circumstances nothing will really happen to spacetime itself - any region of space becomes infinitely big in an infinite amount of time, but gravitationally bound structures and smaller structures held together by atomic forces for example will maintain their identities, just getting further and further apart.

However, a scenario has been mooted called the big rip. This is where the pressure due to the vacuum energy is less than minus the energy density. This is known as phantom energy. Calculations using phantom energy are presented by Caldwell et al. (2003), which suggest that the Hubble parameter will become infinitely large in a finite time. This has the effect of ripping everything apart and spacetime ends in a singularity at some finite time in the future.

At present, observational data are insufficient to rule out the phantom energy scenario. But if there is to be a big rip we know at least that it must be at least many tens of billions of years into the future.

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