# Strong and weak gravitational Fields

1. Sep 8, 2008

### NoobixCube

Hi all,
When working on some GTR derivations the authors of the text make approximations based on the magnitude of the gravitational field. What are the general limits of strong and weak gravitational fields?

2. Sep 8, 2008

### Phrak

From what I've seen in deriving one weak field limit, you begin with a spacetime where the metric is flat; trace(g_uv) = -1,1,1,1. Small perturbations |h_00| << 1 lead to Newton's gravitational potential. Any additions of |h_uv| << 1 to the metric would seem to constitue a weak field limit--if the sign of h_uv is physically permissible. I've put the absolute value around h_uv to avoid making a sign error.

3. Sep 9, 2008

### NoobixCube

Well it came about when deriving the precession of the perihelion of Mercury which does deal with assuming Newtons Solution to the two body problem is a very good approximation. Then when accounting for the General Relativistic equation of motion you have to assume that the Gravitational filed is weak and hence may yield a full solution by assuming a small perturbation to the exact solution for Newtons problem. So you answer touched on my problem, by I was looking for a quantitative value for say a strong field.

4. Sep 9, 2008

### atyy

5. Sep 10, 2008

### Phrak

I don't know of any other meaning to "strong gravitational fields" other than field strengths that cannot be considered weak in the particular analysis in question.

This is somewhat implied by atyy's link, as well. I only glanced at it, but Will's one-size-fits-all rule defining the weak field limit is suspicious.

Last edited: Sep 10, 2008
6. Sep 11, 2008

### NoobixCube

7. Sep 11, 2008

### yuiop

I think one approach would be to take the taylor series or binomial expansion of the equations under consideration. An example given here http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html#c6 of relativistic kinetic energy shows that the first term of the expansion is the Newtonian solution. It is possible to calculate the error "cost" of discarding the other terms or more importantly calculate when the discarded terms become significant. This will of course require you to choose an arbitary error margin that you consider acceptable.

A similar aproximation is shown for gravitational time dilation here http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html#c5 and the discarding of terms with demominator of greater than c^4 possibly provides a natural boundary between weak and strong fields but in the end it is a subjective boundary.