<p>You model the massive object moving through space time. Remember Relativity. In this case I mean just Galilean relativity: The laws of motion are the same in any inertial frame. If I choose a frame that moves with your planet it would mean that the planet does not move at all.</p>

<p>That would make it clear that your model is wrong, a motionless planet should not create a wake in spacetime. Your planet is motionless (wrt to an inertial frame) but is leaving a wake. Your model is incorrect.</p>

<p>Glancing over the code you seem to be dynamically distorting your grid. But really this is a static situation. The grid distortions can be determined for any position of the planet, where the planet has been before should not need to be calculated.</p>

<p>Now this is not spacetime you are describing here, rather this is just Newtonian gravity dressed to look like spacetime. For the sort of mass you discribe here there is no great difference between GR and Newtonian gravity. GR is asymptotically approximated by Newtonian gravity. It is possible to model real spacetime, but it is very computationally intensive. This doesn't make your simulation uninteresting but take care in what is claimed for it. </p>

CC BY-SA 3.0
2015-12-11T22:38:31.870Z
2015-12-11T22:38:31.870Z
James K
<p>To answer the question</p>

<blockquote>
  <p>Does spacetime return to being flat?</p>
</blockquote>

<p>Yes it does. The picture you have calculated is not correct. It is not like that in gravity a solid body plow through spacetime and creates this valley like dragging a bowling ball throw snow would. The curvature of each point is affected by the mass and changes as the mass moves. So if the mass moves away far enough from a given point in space time the curvature becomes flat again.</p>

CC BY-SA 3.0
2015-12-11T09:36:07.190Z
2015-12-11T14:17:12.267Z
2015-12-11T14:17:12.267Z
Sjoerd222888
<p>I wrote an experiment in HTML5 and Javascript to try to show what is happening to the curvature of spacetime as a body moves through a region.</p>

<p>As time progresses, I'm using the <code>g=Gm/r2</code> equation to move the spacetime grid toward the object. When a grid point is within the body, I use <code>g(1-h/R)</code> to modify the bending according to the acceleration at the surface. This assumes uniform density.</p>

<p>The result is that it takes a very large mass and very long time for any sort of noticeable curvature to occur (as you'd expect). By decreasing the Earth's radius by a factor of 3, I was able to see the curvature very well as in the screenshot below.</p>

<p>What occurred to me then is that the the warping of space would remain long after the body of mass had moved on.</p>

<p>Does this warping in space ever return to truly "flat" or is the fact that we almost never orbit through the same absolute region of space mean we never experience this existing warping?</p>

<p>If light went through this "wake" would it bend according to the spacetime curvature created by the long distant planet? Or have I gone wrong in my model?</p>

<p><a href="https://i.sstatic.net/VBRld.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VBRld.png" alt="Spacetime warping demo"></a></p>

<p>This demo uses real values except that the radius is shrunk by 3x to increase its gravitation effect.</p>

<pre><code>earth.radius = 6.371e6 / 3;
earth.mass = 5.972e24;  
spacetimeGrid.extent = 4.5e7;
</code></pre>

<p>You can run the demo here: <a href="https://dl.dropboxusercontent.com/u/2236585/spacetime/index.html" rel="nofollow noreferrer">https://dl.dropboxusercontent.com/u/2236585/spacetime/index.html</a></p>

CC BY-SA 3.0
2015-12-10T21:15:23.107Z
Looks very suspect. Distortions of spacetime should propogate at the speed of light, (effectively infinite at the rate of the simulation) there should be no wake.
James K
CC BY-SA 3.0
2015-12-10T21:24:30.080Z
well, accelerating bodies might produce gravity waves - a prediction of GR not yet experimentally proved, but for normal bodies at 'normal' energies you would not see a wake like this.
adrianmcmenamin
CC BY-SA 3.0
2015-12-10T23:02:54.107Z
@JamesKilfiger I forgot about the fact that gravitational influence also propagates at **c**, so the code is a rather crude approximation of the distortion, and obviously doesn't simulate gravitational waves. Would this ultimately cause spacetime to flatten out?
Nick Bedford
CC BY-SA 3.0
2015-12-14T00:07:22.490Z
We'd live in a very strange universe if the local gravity gradient were affected by a supermassive black hole having passed through the nearby vicinity 12 billion years ago. Spacetime would be riddled with invisible gravitational wellholes of unknown origin.
Wayfaring Stranger
CC BY-SA 3.0
2016-09-11T17:50:57.883Z
What are your axes? Two spaces or one space and one time?
Incnis Mrsi
<gravity><space-time>
Does spacetime return to being flat?
Nick Bedford
# Does spacetime return to being flat?

(Asked by: username_0 on 2015-12-10)

I wrote an experiment in HTML5 and Javascript to try to show what is happening to the curvature of spacetime as a body moves through a region.
As time progresses, I'm using the g=Gm/r2 equation to move the spacetime grid toward the object. When a grid point is within the body, I use g(1-h/R) to modify the bending according to the acceleration at the surface. This assumes uniform density.
The result is that it takes a very large mass and very long time for any sort of noticeable curvature to occur (as you'd expect). By decreasing the Earth's radius by a factor of 3, I was able to see the curvature very well as in the screenshot below.
What occurred to me then is that the the warping of space would remain long after the body of mass had moved on.
Does this warping in space ever return to truly "flat" or is the fact that we almost never orbit through the same absolute region of space mean we never experience this existing warping?
If light went through this "wake" would it bend according to the spacetime curvature created by the long distant planet? Or have I gone wrong in my model?

This demo uses real values except that the radius is shrunk by 3x to increase its gravitation effect.
earth.radius = 6.371e6 / 3;
earth.mass = 5.972e24;  
spacetimeGrid.extent = 4.5e7;

You can run the demo here: https://dl.dropboxusercontent.com/u/2236585/spacetime/index.html

**Tags:** gravity, space-time

> **Comments:**
> **username_1**: Looks very suspect. Distortions of spacetime should propogate at the speed of light, (effectively infinite at the rate of the simulation) there should be no wake.  
> **username_2**: well, accelerating bodies might produce gravity waves - a prediction of GR not yet experimentally proved, but for normal bodies at 'normal' energies you would not see a wake like this.  
> **username_0**: @JamesKilfiger I forgot about the fact that gravitational influence also propagates at **c**, so the code is a rather crude approximation of the distortion, and obviously doesn't simulate gravitational waves. Would this ultimately cause spacetime to flatten out?  
> **username_3**: We'd live in a very strange universe if the local gravity gradient were affected by a supermassive black hole having passed through the nearby vicinity 12 billion years ago. Spacetime would be riddled with invisible gravitational wellholes of unknown origin.  
> **username_4**: What are your axes? Two spaces or one space and one time?  

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## 2 answers

### Answer by username_1 on 2015-12-11. Score: 3

You model the massive object moving through space time. Remember Relativity. In this case I mean just Galilean relativity: The laws of motion are the same in any inertial frame. If I choose a frame that moves with your planet it would mean that the planet does not move at all.

That would make it clear that your model is wrong, a motionless planet should not create a wake in spacetime. Your planet is motionless (wrt to an inertial frame) but is leaving a wake. Your model is incorrect.

Glancing over the code you seem to be dynamically distorting your grid. But really this is a static situation. The grid distortions can be determined for any position of the planet, where the planet has been before should not need to be calculated.

Now this is not spacetime you are describing here, rather this is just Newtonian gravity dressed to look like spacetime. For the sort of mass you discribe here there is no great difference between GR and Newtonian gravity. GR is asymptotically approximated by Newtonian gravity. It is possible to model real spacetime, but it is very computationally intensive. This doesn't make your simulation uninteresting but take care in what is claimed for it.


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### Answer by username_5 on 2015-12-11. Score: 3

To answer the question

> Does spacetime return to being flat?

Yes it does. The picture you have calculated is not correct. It is not like that in gravity a solid body plow through spacetime and creates this valley like dragging a bowling ball throw snow would. The curvature of each point is affected by the mass and changes as the mass moves. So if the mass moves away far enough from a given point in space time the curvature becomes flat again.


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