How does the GR field equation reduce to Newton's law of gravity?

In summary, the conversation is about the topic of General Relativity and the search for a link between Einstein's equations and Newton's law of gravity. The person is interested in finding a proof or derivation and is provided with a link to a lecture and a chapter on the subject. They are also directed to a Wikipedia page for further information.
  • #1
Geezer
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I've never taken a class on GR, but I've been looking at books on the subject.

Clearly, Einstein's equations for GR must reduce to Newton's law of gravity, but how? I haven't seen it worked out anywhere. Can someone send me a link, or show a proof or derivation?

Like I said, it's not homework or anything; I'm just interested in seeing how it's done.

Thanks,
Geez
 
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  • #2
Lecture 10 http://people.maths.ox.ac.uk/~nwoodh/gr/index.html

Chapter 24 http://www.pma.caltech.edu/Courses/ph136/yr2006/text.html
 
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Related to How does the GR field equation reduce to Newton's law of gravity?

1. How does the GR field equation relate to Newton's law of gravity?

The GR field equation, also known as Einstein's field equation, is a mathematical formulation of Albert Einstein's theory of general relativity. This equation describes the curvature of spacetime in the presence of matter and energy. When solved for a specific scenario, such as a single massive object, it reduces to Newton's law of gravity.

2. Why does the GR field equation reduce to Newton's law of gravity for a single massive object?

When there is only one massive object present, the curvature of spacetime is not significant enough to have a noticeable effect. Therefore, the GR field equation simplifies to the simpler Newton's law of gravity, which describes the gravitational force between two objects based on their masses and distance.

3. How does the GR field equation account for the observed discrepancies with Newton's law of gravity?

Newton's law of gravity was formulated based on observations of the motions of objects in our solar system. However, it does not accurately describe the behavior of objects at extremely high speeds or in strong gravitational fields. The GR field equation incorporates these factors and provides a more accurate description of gravity in these scenarios.

4. Can the GR field equation be used to make predictions about the behavior of objects in space?

Yes, the GR field equation has been used to make predictions about the behavior of objects in space, such as the bending of starlight by massive objects and the existence of black holes. These predictions have been confirmed through observations and experiments, providing strong evidence for the validity of the GR field equation.

5. Does the GR field equation completely replace Newton's law of gravity?

No, the GR field equation does not completely replace Newton's law of gravity. While it provides a more accurate description in certain scenarios, Newton's law of gravity is still used in many practical applications, such as calculating the trajectories of objects in our solar system. Additionally, Newton's law of gravity is easier to use for simple calculations and remains a fundamental concept in the study of gravity.

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