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I don't think that this is experimentally testable due to it not being physically possible to recreate anything like the below video. But, you can see that when the Sun disappears the curvature created by it resets according to the speed of light:

https://www.youtube.com/watch?v=xd8GnggiKg0

However, I'm not really convinced this is true, it seems like gravitational waves (which travel at the speed of light) are "packets" of energy traveling through space, and this hypothetical situation would be purely affecting the curvature of the spacetime.

Don't know how to properly word my question according to the correct terminology, hope it makes sense. Basically would just like to know if this is impossible or just not able to be determined.

MFerguson
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There is no rule against things "changing faster than the speed of light". For example, the universe is cooling everywhere at the same time. There is no need to wait for the temperature change to propagate through the intergalactic medium.

However, causal influences do not travel faster than light, and your source is correct that the gravitational consequences of any change to the Sun's state would only travel at the speed of light. The universe only cools everywhere because that cooling is driven independently by the same process (adiabatic expansion) everywhere. Or in the example of a warp drive given in the other answer, although the "warp bubble" represents spacetime curvature that travels faster than light (in some sense), it has to be prepared in advance and does not propagate on its own.

Sten
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Yes. There’s no reason it can’t move faster than light.

Gravitational waves propagate at $c$ because of how spacetime geometry works - if you interpret the wave equation in the way you need to, you get a speed of $c$ for it. But spacetime curvature in general can travel at any speed.

What you are not allowed to do is send objects along spacelike curves. Things in general (photons, protons, etc) are not allowed to do that (in fact nothing really is) because if you travel along spacelike curves you’re going to a) experience imaginary proper time (bad) and b) be able to back up into your own past and screw with causality. Very bad. However space can be curved so that I can go at any speed without getting onto a spacelike curve (as Paulina mentions, this is the basis for the Alcubierre drive, among others). In flat spacetime, any curve going faster than $c$ is spacelike, but in Alcubierre spacetime within the warp bubble, most curves with any speed are timelike, meaning that I as a massive human being can travel them safely.

Note that the Alcubierre drive doesn't actually let you go faster than a photon - it just speeds up photons, so the speed limit is increased. This is the case with other warp drives as well.

So it’s easy to get curvature to go faster-than-light. Sometimes that curvature requires negative energy, which we can’t get to, but there are contrived circumstances where curvature allows for faster-than-$c$ speeds. Most of the time and especially in flat space curvature changes at around $c$ naturally, though.

controlgroup
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