Does time obey the inverse square law?

[D.S.Beyer]

We have all seen the graphs of space time. The ones that look like a bowling ball pushed into a bed. But what are those graphs really saying?

Are they descriptions of gravitational force? Or simply a visual aid to describe the path that light follows around the body of mass?

My question is where can I find a graph depicting the dilation of time around bodies of mass? And does time obey the inverse square law?

I realized I have been looking at these graphs my whole life and never really understood what they mean. Help me out Physic Forums!

 

[DrGreg]

You are right, the "bowling ball pushed into a bed" diagrams show only space curvature; they don't show spacetime curvature, so really they don't explain all that much.

For a start, you might try the diagram at http://www.relativitet.se/spacetime1.html. (Don't take it too literally -- it's not supposed to imply that time is circular!)

 

[Nabeshin]

They are visual aids, do not take them too literally because there are many many caveats associated with them.

I've hosted an image from a movie I recently made which sort of describes what you're talking about http://i41.tinypic.com/w9740w.jpg". This is a scenario where two black holes are spiraling together. So, the color of the surface, the lapse, corresponds to the relative rate of time passage. As you can see, far away it is ~1, meaning time is flowing at the normal rate. However near the holes it goes down to only about .4 the time rate at infinity.

If you have any questions about this in particular don't hesitate to ask!

 

[D.S.Beyer]

Thanks for replying. What I am after is a "time-well" graphical representation.
I have found lots of time dilation graphs but no gravitational time dilation graphs.

I am a very visual person and would simply like to see the passage of time represented in the same fashion as the gravity well. Does anyone know of some software that will help me with this?

 

[Ich]

You need some software capable of showing "3D" graphs.
The formula for time dilation (clock rate relative to clock rate at infinity) is
\sqrt{1-\frac{2M}{r}}
For large r, this is approximately going as (1)-1/r, not 1/r².
For the interior of the gravitating body, it looks more like a parabola.
All in all, similar to your graph C.