I Modifying EFE to Match Newton's Gravity Predictions

[haushofer]

I don't understand this. What does the invariant speed have to do with time derivatives? In the c infinite limit, under several schemes, you have Newtonian gravity. Does that mean time derivatives can't exist in Newtonian physics??

Note, the c infinite limit of the Lorentz transform is the Galilean transform. Does that prevent time derivatives from existing?

I meant coordinate time derivatives on the metric, sorry for the confusion. These are multiplied by a factor 1\c and so constitute factors which drop out after the c-->oo limit. Of course, this has nothing to do with the derivatives in the geodesic eqn. w.r.t. the affine parameter ;)

 

[PAllen]

The Einstein-Infeld-Hoffman equations aren't differential equations. They are the Newton force equation, $G m_1 m_2 / r^2$, plus first-order post-Newtonian corrections, summed over all pairs of bodies. Since the post-Newtonian correction terms are all multiplied by $1 / c^2$, they all vanish in the limit $c \to \infty$, leaving just the Newtonian force.

How are they not differential equations? They relate positions and first and second derivatives thereof. For n bodies, they are a system of n complicated second order differential equations. The Newtonian case is the same, only the equations are much simpler and of course are explicitly solvable for n=2.

 

[PeterDonis]

How are they not differential equations?

You're right, I was only looking at the RHS of the Newtonian case.