Does Gravity Have a Speed Limit?

[Astro_Will]

Does gravity have a finite speed at which it effects an object. For example (and this is strictly hypothetical) if a new star were to suddenly appear near the orbit of Saturn would Earth instantly notice the influence or would it take a few minutes? When I think of Newtonian gravity I would just assume it travels at c so we would notice the gravitational effects the same time we saw the light from that star. But with relativity I'm really just not sure because I don't know if the bending of spacetime has any speed limit. I hope I'm making myself clear here.

Also: If gravity does travel at c is that only in a vacuum?

(Also an explanation of the graviton and what that means for the idea of spacetime would be appreciated)

 

[jtbell]

See the first entry in "Frequently Asked Relativity Questions" at the top of this forum.

Then if anything there needs to be clarified, ask away!

 

[PeterDonis]

Does gravity have a finite speed at which it effects an object.

This forum has a FAQ on this:

https://www.physicsforums.com/showthread.php?t=635645

Also, the Usenet Physics FAQ gives a good overview:

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

For example (and this is strictly hypothetical) if a new star were to suddenly appear near the orbit of Saturn

This is not just hypothetical, it's impossible. A star can't appear out of nowhere; that would violate conservation of energy. That means we can't even formulate a consistent mathematical model in General Relativity of what you are trying to describe. It turns out to be somewhat tricky to formulate a scenario that captures what we intuitively think of when we think of "changes in gravity propagating", and can also be consistently modeled in GR. However, when we do, as the FAQs above note, the answer we get is that gravity propagates at the speed of light.

When I think of Newtonian gravity I would just assume it travels at c

No; the speed of gravity in Newton's theory is infinite. Just look at the expression for gravitational force:

$$F = \frac{G m_1 m_2}{r^2}$$

The $m_1$, $m_2$, and $r$ in that equation are all evaluated "right now"--in Newton's theory there is absolute space and absolute time, so "right now" has a well-defined meaning. So if any variable changes, the entire Universe instantly "sees" the change. This is the main reason why Einstein, once he had come up with Special Relativity, had to then come up with a new theory of gravity--General Relativity: the old theory of gravity, Newton's, was obviously incompatible with relativity.

If gravity does travel at c is that only in a vacuum?

I don't know that this aspect of the question has really been considered; all of the treatments that I'm aware of only talk about gravitational waves (which are the way changes in gravity propagate) in a vacuum.

 

[Astro_Will]

No questions. Thanks for this. I'll be sure to check the FAQ first from now on.

 

[bcrowell]

Also: If gravity does travel at c is that only in a vacuum?

http://physics.stackexchange.com/questions/12944/metamaterials-for-gravitational-waves