Comparing two sources one has ##\frac{d^{2}x^{i}}{dt^{2}}=-\frac{1}{2}\epsilon\bigtriangledown_{i}h_{00} ## and the other has ##\frac{d^{2}d^{i}}{dt^{2}}=\frac{1}{2}\epsilon\bigtriangledown^{i}h^{00}##, And the one using the lower index has the Newton-Poisson equation as ## \frac{d^{2}}{dx^{i}}=-\bigtriangledown_{i}\Phi ## and the source using the upper index for the partials has ## \frac{d^{2}}{dx^{i}}=-\bigtriangledown^{i}\Phi ##. I.e- there is no sign change in the Newton-Poison equation.(adsbygoogle = window.adsbygoogle || []).push({});

Questions:

- Thus they are led to the same identification of ##g_{00}## but differering by a sign- how is the physics unchanged?

- I'm really confused about what this raisin and lowering partial derivative means- I know that the contravaiant and covariant derivaitve differ in their definition for the sign of the connection term, however the partial derivative term has the same sign in both cases.

- Why is there no change in the Newton-Poisson equation, is it because the operators ##\bigtriangledown ## are denoting differnt things in Newtonian mechanics and GR? So in Newtonian mechanics it's just partial derivatives. How is it differing in the GR sense?

Thanks in advance.

(The two sources are Tod and Hughston, intro to GR, and http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken] )

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# Weak Field Appox, sign question, raising lowering partial derivativ

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