Strong and weak gravitational Fields

In summary, the conversation discusses approximations made in GTR derivations based on the magnitude of the gravitational field. The limits of strong and weak fields are determined by the flatness of the metric and the magnitude of perturbations. The weak field limit is defined in section 4.1.1 of Clifford Will's article, but the exact value for a strong field is subjective and based on an arbitrary error margin.
  • #1
NoobixCube
155
0
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?
 
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  • #2
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.

Is this what you're asking?
 
  • #3
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
Try section 4.1.1 of Clifford Will's article:
http://relativity.livingreviews.org/Articles/lrr-2006-3/ [Broken]
 
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  • #5
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.
 
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  • #6
atyy said:
Try section 4.1.1 of Clifford Will's article:
http://relativity.livingreviews.org/Articles/lrr-2006-3/ [Broken]
I will have a read thanks for your responses.
 
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  • #7
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.
 

1. What is a strong gravitational field?

A strong gravitational field is a region in space where the gravitational force is significantly higher than in other areas. This can be caused by the presence of a massive object such as a planet or star.

2. How is the strength of a gravitational field measured?

The strength of a gravitational field is measured by its gravitational acceleration, which is the rate at which objects fall towards the center of the field. This can be calculated using the mass and distance of the objects involved.

3. What is the difference between a strong and weak gravitational field?

A strong gravitational field has a higher gravitational force and acceleration compared to a weak gravitational field. This can also affect the curvature of space-time, with stronger fields causing more severe distortions.

4. How do strong and weak gravitational fields affect objects differently?

In a strong gravitational field, objects will experience a greater gravitational force and acceleration, causing them to move faster and potentially orbit or fall towards the source of the field. In a weak gravitational field, the effects will be less noticeable and objects may experience a smaller gravitational force.

5. Can a strong gravitational field exist without a massive object?

No, a strong gravitational field cannot exist without a massive object. The strength of a gravitational field is directly proportional to the mass of the object creating it. Without a massive object, there would be no significant gravitational force or acceleration in that region of space.

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