Gravitational Potential & Field: Doubts & Solutions

[BruceW]

Nugatory has explained it very well. When wikipedia says: "The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity." This is only a loose analogy. The two relationships are not meant to be taken as literally identical.

Edit: Also, on this page: http://en.wikipedia.org/wiki/Einstein_field_equations They give a derivation of Newton's law of gravity from Einstein's field equations, under several limiting assumptions. So from looking at this derivation, you can see in what sense the stress-energy tensor in general relativity and the mass density in Newtonian gravity are similar.

 

[MikeGomez]

Yes, but I personally think that including other fictitious forces in gravity is more or less justified by the equivalence principle. However, since there isn't general agreement on the topic and since my justification is admittedly pretty sketchy I certainly don't push my viewpoint.

Hmm, I don't know much about Christofel symbols, but I was under the impression that fictitious forces in gravity are justified by the equivalence principle.

You say there isn't general agreement on this, so it would be interesting if you could please provide some references to those arguments.

 

[Dale]

Hmm, I don't know much about Christofel symbols, but I was under the impression that fictitious forces in gravity are justified by the equivalence principle.

If you have a curvilinear coordinate system and you parallel transport a vector then its components will change, not due to any change in the vector itself, but due to the curving of the coordinates. The Christoffel symbols capture that effect.

You say there isn't general agreement on this, so it would be interesting if you could please provide some references to those arguments.

I think that MTW gives a good overview in "Gravitation". You should start around p 460-470 or so. Here is an online source: http://arxiv.org/abs/physics/0204044

 

[MikeGomez]

Thanks Dale.