# Time dilation explanation for gravity?

1. May 18, 2008

### yuiop

Hi,

I seem to recall reading a post a long time ago (that I cannot find) that gravity in the Newtonian limit (eg the Solar system) can be completly explained in terms of time dilation alone. Is that true and if so, how does that work?

2. May 18, 2008

### Mentz114

In the weak field limit, when GR goes to Newtonian gravity, a function of g_00 acts like the potential, and g_00 is the time dilation factor ( or it's square root).

In fact,

$$-g_{00} = 1 + \frac{2\phi}{c^2}$$

Is this what you mean ?

Last edited: May 18, 2008
3. May 18, 2008

### yuiop

Not sure. Assuming $$\phi = GM/R$$

and $$-g_{00} = 1 + \frac{2GM}{Rc^2}$$

is obtained from the binomial aproximation of $$\frac{1}{\sqrt{1-2GM/Rc^2}}$$

How is the Newtonian of gravitational potential of -2GM/R obtained from that?
Where do the +1 and c^2 go and how is the inverse square law of gravity recovered?

Also, as I understand it. GR does not have gravitational forces acting on a free falling body, but there still are gravitational forces acting on a stationary body. Does GR alter the force felt by a stationary body or is it the usual GM/R^2?

4. May 18, 2008

### Mentz114

Kev,
it takes four pages to demonstrate properly, but if you start with the EFE with a simple source, and let most of the gradients involved disappear, then solve the equations of motion you get an inverse square force law, with a function of g_00 playing the part of the potential. Newtonian gravity is recovered in full. Quite a triumph, in fact.

In my earlier post, phi is not the Newtonian potential, but a function of it.

Here's a good explanatory article.

http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken]

Last edited by a moderator: May 3, 2017
5. May 18, 2008

### mojocujo

If you want to use GR without a curved spacetime you have to to alter the constants that GR uses like C and the planck length and make them rubbery. You can then use euclidian flat space still using G as a constant.

6. May 19, 2008

### Mentz114

Sounds dodgy to me. GR does not have a length scale. Care to elucidate ?