# A theoretical Q about gravity

I "know" that gravitic effects have been shown to work at the speed of light. This meaning, if the sun were to disappear the earth's orbit would change approximately 8 seconds later, the time it takes for light to reach earth. I believe this is correct, no?

Now let us take the same situation, the Sun vanishing from existence. I know this is hardly possible in any way. But its merely for this question so please bear with me. The sun disappears. If you had some method of measurement for measuring the instantaneous "force" or rather the "curvature of space" due to gravity, and you took said device and placed it really close to the surface of the sun, it would read quite high correct? Assuming gravity is something along the scale of 1/r^2 seems like it would max when r is min. So assuming this is correct, yes? We move on.
The sun dissappears. Now we know that the measurement near the sun was reading high, and a measurement near the earth (due to the sun) not as high.
Now does each measurement device (assuming very very accurately updated) go from their respective measurement INSTANTLY to "0" as the "effect" wave travels from suns point out to the measuring devices, or does it go from the value to 0 through a function thats dependent on time.

I think about this thought problem back to a bowling ball on a rubber sheet. If you take the bowling ball away instantly, the rubber sheet doesnt just teleport back to its flatness, but goes through a quick continuous change from deformed to normal (that i believe would be as if the bowling ball got lighter at a very very rapid pace).

Does space follow a similar principle? What would the sun disappearing look like in terms of a planar surface if you had to animate it?

EDIT:
After re-reading im thinking of a way to define my idea of instantaneous.
The only way i can ask this question in my head is how would you see it as an animation if it was a 2D universe. (so you can use 3rd to show curvature.)

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Using the rubber sheet analogy, if the sun disappeared, a ripple-like wave will move out from the centre and gradually decay to leave flat space.
Gravitational waves.

Ok good. My main question is : Does any time pass between from the instant when the sun disappears to when a measurement device at the center of the sun measures space curvature restored. I know if you go farther away the time it takes for the gravity wave to hit the far-device is just the lightdistance.
My question is tough to describe because a measurement device at the center of the sun would not have force in any specific direction but rather all directions of possible motion. Its potential would be at 0. Its movement at 0. BUT there would be some gravitational pull to KEEP it at 0 potential. Perhaps this imaginary device can measure whether there is still a restorative force in action. Then my question becomes, is there any period of time between when this device measures that it is at the bottom of a gravitational well to when it is at 0 curvature.

I "know" that gravitic effects have been shown to work at the speed of light. This meaning, if the sun were to disappear the earth's orbit would change approximately 8 seconds later, the time it takes for light to reach earth. I believe this is correct, no?

it takes 8 minutes for light to get here from the sun.

er, thats what i meant. Im sorry. Regardless, my questions still stands, can anyone help?

You should check out the thread 'Is a uniform gravitational field ...' in this forum. I'm no longer even sure my earlier reply is correct.

I looked it over and though fascinating it couldn't really answer my question.
I guess the most refined-simplest way to ask it is:

At what rate does space-curvature restore itself in absence of a once-present mass?

I'm not talking about the speed of the radial effects, but rather the center point of a gravitational well that once existed.

I've just been thinking about it a lot and racking my memory to see if i've already learned this or even heard about it and I can't find anything. I'm SURE someone MUST have asked this question before. And I feel as if the answer could be : It changes as fast as the mass is taken away. But I dont FEEL like that would be right, due to the lagginess of gravity in the radial aspect, why wouldn't there be a slight delay, or rather a continuous change from curvature to none.
I'm hesitant to speculate much further due to approaching anything that could be construed as a personal theory. My personal theory is that I don't know enough to make personal theories. And so I just ask questions.

I'm rewording my original post to reflect something I posted on another site. I'll leave the original up there but this may be a little more clear.

I'll try to articulate this question as carefully as possible to avoid redundancies and confusion. I will also put a thought experiment (purely hypothetical) afterward to explain what I am asking.

Main Question : At what speed does gravitational space curvature restore itself after the removal of mass?

Hypothetical : (On a large scale) The sun disappears. Does the immediate topology of space near the sun's mass's locations return to "0" (Flat) or does it take ANY quantity of time.

This is not a question about the speed at which gravity asserts itself. And that is, as far as I know (and most GR/Q Theorists agree) that gravity, like EM, travel at the speed of light. (Please don't misunderstand the usage of "travel" here. I mean simply the delay at which it's effects are observed).

So as another thought experiment, imagine the universe as a 2D rubber sheet. I hope this can approximately describe some nature of spacetime. There is a bowling ball resting "in" it thus giving it a potential curvature well. Upon INSTANT (I know, I know, instant is tough to comprehend, but hypothetical!) upon INSTANT removal, the rubber sheet would restore itself to flat as fast as it's nature allows (being affected by its properties).

If we treat space similar to this, is there a time of restoration, or is it also instantaneous. The 2D model is convenient due to the ability to use a real-metric 3rd dimension to measure some "distance" traveled by the potential well over time. Since this "distance" seems to be merely the potential STRENGTH, is there some differential to describe the change in strength of a gravitational field upon mass removal over the change in time?

If there were by chance some constant say K = dStrength/dt I wonder how it would relate to the permittivity and permeability of space and what further knowledge could be extracted from such a relation. Does anyone know how regular materials behave? Say rubber for instance?

Thanks for your help. And please, if you know it, feel free to use any mathematics or references you know to help explain. I have a degree in physics and minor in mathematics so i feel nothing is beyond my understanding, merely beyond my knowledge.

vanesch
Staff Emeritus
Gold Member
This is a question that comes up regularly:
"what would happen gravitationally if the sun just disappeared ?"

The answer is that general relativity has no answer to that question, for the simple reason that in GR, the sun cannot instantaneously disappear.

This is analogous as to:

"What EM waves would be emitted if a charge just disappeared ?"

The Maxwelll equations have no answer to that either, because from the Maxwell equations, you can derive conservation of charge, so it cannot disappear without going somewhere else. If you try to force this onto the Maxwell equations, you get an inconsistent set of equations.

It is the same in GR.

How about then, this should be more "possible" if not probable:

A star is traveling at 0.999c. The star is quite massive. Does the curvature it makes in space fit completely as if it would be standing still (From an external viewpoint, someone standing still), and travel with the star. Is there no "short" side on its direction of travel and no "laggy" long side behind it as you could imagine if there was a delay.
The real question i'm trying to find out is does an area of great curvature restore to flat as quickly as an area of less curvature or is there a difference.

Good question. I'm guessing that you're asking if, in case of the sun dissappearing, the "wave front" carrying the change in spacetime geometry would make everything it hits revert to flat Minkowski space or that there are intermediate forms. Honestly, I have no idea but I wonder if anyone else has considered the question.

Exactly. I wondering if you had it disappear and you were to ignore that there was a mass there and just watched the curvature of spacetime would it spring back to flat as if it were a step function, starting at the center and working outward radially at C. Or would it do something similar radially but the curvature would have some "change" over time. And not be instantaneous.

I've been thinking about it the last few minutes, and it's really a hard problem. It's tough enough to get wavelike solutions to Einstein's equations, the heart of general relativity (all kinds of technicalities like gauge choices etc...) without forcing it to go from a Swartzschild metric (like there is around the sun) to a Minkowski one. I'll let you know if I find something that deals with this, but I doubt that I'm smart enough myself.

EDIT : One thing I can say for sure is that it wouldn't be "instantenious" since something like a step function is not allowed in GR, it needs to vary smoothly. The interesting question is what shapes it takes on inbetween. My gut feeling is that pretty much anything goes and that alot depends on the boundary conditions (distribtution of the matter of the other celestial bodies and so forth).

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I'm not only interested in what shapes it takes between the two extremes, but also the speed of progression through the changes. With the rubber sheet analogy we're afforded the luxury of a measurable 3rd spacial dimension with which to gauge the depth of curvature and then the change in that depth. Do we have some measurable 4th dimension (spatial or non) with units akin to 3D to gauge the depth of curvature in 3D as you would with the rubber sheet?
I can picture it in my head (sort of tough) but can't think of what sort of units you could possibly use that isn't just a measurement of deformation (light bending around a star). I assume this is due to our being limited to measuring in 3d.

Once again i'm trying NOT to approach personal theory. Just asking questions about things I do not know, and putting up hypotheticals that are attached to the possible explanations in my head.

If there were some delay in the deformation and reformation of spacetime due to masses moving, is it possible that these effects could be seen near masses at relativistic speeds. Almost like a Doppler effect on the gravitational "waves". Since in front of the mass gravity wouldn't have had a chance to curve the space, and leaving behind it a "ghost" image of curvature. Unfortunately I feel that if this is where this train of thought is heading it leads us to some sort of space-medium (ether) that has been disproven. But that doesn't mean space doesn't have any resistance to bending, does it? It must, that seems to be the whole effect of what MASS is, the "force" required to "bend" space to a relational curvature.

I know I don't know enough about spaces and manifolds to be able to ask these questions clearly, but until I get accepted into grad school and have an opportunity to learn about it I'm left in the dark, and that's just unacceptable to me.
Thank you all for helping me figure this out.

I'm not only interested in what shapes it takes between the two extremes, but also the speed of progression through the changes..

This is actually though to answer conceptually, and even ill-posed. You see, what you do with GR is find a solution to the Einstein equations given a certain mass/energy distribution. That solution is a certain spacetime. If I understand you correctly, you seem to be asking how the 3 spacial dimensions will change throughout the process. The problem is that we perceive a 3D slice of the 4D spacetime, and that the slice depends on the observer. So one observer could see the "rippling space" in one way, and another could see it another way. The 4D spacetime is really the fundamental thing and the 3D part we see is dependent on perspective.

Gell Model

Hi there.

Whenever I think of, or rather visualize, objects in space curvature, I see balls in a sea of clear gell. Each ball pushes the "gell" away with an outward force; perhaps gravity is as much a repulsion as it is an attraction. The dominant mass will of course be the main attractor-resister, and each ball that orbits has its own outward force as well, like magnets pushing against one another.

So when the [Sun] dominant object is removed -- in this case "phased" out -- the gell will fill-in the empty space, consistent with whatever rate the object was "removed".

With the largest attractor-resistence now gone, neighboring objects will actually be "pulled" toward the void, like a tide, until a new inertial paradigm occurs.

I imagine that the sun's rays would tell us before the "gell" would, so it would be felt after the lights go out.

Make any sense?

A star is traveling at 0.999c. The star is quite massive. Does the curvature [..have] no "short" side on its direction of travel and no "laggy" long side behind it as you could imagine if there was a delay.
The real question i'm trying to find out is does an area of great curvature restore to flat as quickly as an area of less curvature or is there a difference.

Unfortunately, I don't think this scenario will answer your real question (though as has already been said, GR predicts all changes are smooth and propagate "at the speed of light", which would suggest that smaller disturbances dissipate sooner.. if you could find an example of such a disturbance). Even in electromagnetism, the electric field doesn't really lag behind a charge... and keep in mind that every single star is travelling at 0.999c, from something's perspective.

vanesch
Staff Emeritus
Gold Member
How about then, this should be more "possible" if not probable:

A star is traveling at 0.999c. The star is quite massive. Does the curvature it makes in space fit completely as if it would be standing still (From an external viewpoint, someone standing still), and travel with the star. Is there no "short" side on its direction of travel and no "laggy" long side behind it as you could imagine if there was a delay.
The real question i'm trying to find out is does an area of great curvature restore to flat as quickly as an area of less curvature or is there a difference.

I don't understand your question. Consider the sun, and an electron in some LEP collider or whatever traveling at 0.999c. In the electron's reference frame, the sun is now traveling at 0.999c. But that's just a different coordinate system to describe the same spacetime manifold!

Well, lets say we're standing still and watching a star travel at 0.999c across our field of vision. If there were some way to measure observable gravity at a distance, would there be any relativistic effects to its field/curvature? It seems like there should be. E&M waves are affected by relativist speeds aren't they?
I'm not saying that there'd be some difference in the star's reference frame, but rather in ours.

Are you trying to say that the object moving or disaperaing will cause some kind of wake like when a boat moves in water before the water returns to normal and you are interested in the size of this wake and how long it takes to return to normal.

Kind of like a damped oscillation. But for damping doesnt there need to be an external force applied to the system?

What would this force be?

Is there some kind of tension for gravity similar to when you hold a sheet with a ball on if you hold it tight the sheet will not dip much but if its loose the ball will sink more.
The size of this tension would surely determine how fast it resorts to a flat sheet kind of like permeability of a gravitational field where instead of how it supports a magnetic field it would refer to how space can support a gravitational field?

This make any sense?

Alex

Are you trying to say that the object moving or disaperaing will cause some kind of wake like when a boat moves in water before the water returns to normal and you are interested in the size of this wake and how long it takes to return to normal.
Kind of like a damped oscillation. But for damping doesnt there need to be an external force applied to the system?
What would this force be?
Is there some kind of tension for gravity similar to when you hold a sheet with a ball on if you hold it tight the sheet will not dip much but if its loose the ball will sink more.
The size of this tension would surely determine how fast it resorts to a flat sheet kind of like permeability of a gravitational field where instead of how it supports a magnetic field it would refer to how space can support a gravitational field?
This make any sense?
Sincerely, I don't know; however, making an analogy with sound waves propagating in a solid medium, the elasticity of the medium is related to the sound's speed in it, so maybe it's the same with gravitational waves (which propagate at light's speed).