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?
