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When this sphericall shell contracts or expands, the clock inside contracts and expands too?

I want to know if the clock becames larger or smaller, faster or slower when the shell pulsates.

This is an ideal shell, a special shell, massive and sphericaly symmetric thin shell.

Here: https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativity) , we can see this:

"The conclusion that the exterior field must also be stationary is more surprising, and has an interesting consequence. Suppose we have a spherically symmetric star of fixed mass which is experiencing spherical pulsations. Then Birkhoff's theorem says that the exterior geometry must be Schwarzschild; the only effect of the pulsation is to change the location of the stellar surface. This means that a spherically pulsating star cannot emit gravitational waves."

The same it happens with our ideal sferical shell.

But about pulsations, Birkhoff´s theorem doesn't say what it happens inside the shell, only that the field there is null, as Newton said too.

I would want to know what it happens with the clock inside when the shell pulsates.

Here: Does a massive spherical shell expand the time inside itself? ,we can see, that @timm and @Árpád Szendrei say that time inside a shell is the same at outer surface, because this it depens only the external potential. I agree and think that besides the time, space are the same in this two places (inside and outside) too.

My conclusion is that when the spherical shell expands or contracts, the tic-tacs within it "accelerate or brake" while the lengths contract or expand respectively.

So a special sphericall shell can produce gravitacional waves inside itself.

Is it okay to think so?

João Bosco
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  • It depends on for what purpose you want to use the shell, but usually no. – garyp Sep 24 '18 at 01:49
  • Supposing that you did have a spherical shell of distant stars around the Earth, there are plenty of things that would prevent its collapse: for instance, the stars in the shell could have some angular momentum; alternatively, space could be expanding; alternatively, the material outside that shell could exert a greater gravitational force than the material inside. – probably_someone Sep 24 '18 at 02:02
  • given the shape of the Milky Way as a disk, this is likely not a useful assumption. – ZeroTheHero Sep 24 '18 at 02:16
  • Seems like you're basically asking about why a Big Crunch hasn't happened yet. – Nat Sep 24 '18 at 02:32
  • @ZeroTheHero - I asked this question because it seems that for any point in the universe, independly its position, the distant stars "work" as if they form a spherical shell, but I'm not sure if this is correct. – João Bosco Sep 24 '18 at 03:05

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You can't think of the stars, even the naked-eye visible ones, as being in a spherical shell.

Wikipedia provides a list of the brightest stars (as seen from Earth) and ignoring the Sun, these 92 stars range from being 4.4 light years to 2600 light years away, so not a shell, but a sphere.

What stops them falling on Earth is simply that they are all in motion about the galaxy, more or less in a similar way. It's essentially the same reason the planet's don't fall on the Sun - they are in orbit.

The galaxy is very large (diameter 100,000 light years) and even a 2600 light year sphere is a very small region on that scale. The objects in that sphere have broadly similar orbits (although over long timescales they'll get a little closer and farther away from each other). The attraction of these individual stars to each other is nowhere near enough to overcome their general orbital motion within the galaxy.

One of the closest approaches by another star was about 70,000 years ago when a star called Scholz's Star came within about 2 light years of the Sun, compared to it's current distance of about 20 light years. Even then the attraction between that star and the Sun was not enough to overcome their orbital motion within the galaxy so there was no chance of a collision.

StephenG - Help Ukraine
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  • If there were a hole in the center of the Earth with 1 meter radius (for example), Our planet would act as a spherical shell for any small object placed in this center. I think the same thing happens when you think about the distant stars. – João Bosco Sep 24 '18 at 03:20
  • What you're not allowing for (in terms of stars and Earth) is the idea of parallax which is something obvious to astronomers long, long ago. You're thinking in terms of a static sphere, but with Earth's motion about the Sun, there's a parallax we see and we can tell we're moving moving within your notional sphere. – StephenG - Help Ukraine Sep 24 '18 at 03:31
  • But if you circle the small object in the hole (hypothesis) of the center of the Earth, there is also parallax in relation to the parts of the Earth – João Bosco Sep 24 '18 at 03:43
  • Correct, although there is a lot less when comparing the diameter of the Earth ( 12700 km ) compared to the baseline of the diameter of Earth's orbit ( 300,000,000 km ). The difference in angle is some 23,600 times larger when using Earth's orbit compared to just it's diameter alone. One can be seen relatively easily, but the smaller one is very hard to detect. – StephenG - Help Ukraine Sep 24 '18 at 03:56