In this documentation from Nasa a procedure to get to what I guess is the gravitational acceleration according to the post-Newtonian expansion at the 1PN-level for the spherically symmetric case is found:(adsbygoogle = window.adsbygoogle || []).push({});

http://descanso.jpl.nasa.gov/Monograph/series2/Descanso2_all.pdf [Broken]

The procedure is based on using the metric shown in expression (4.60) on page (4.42). The metric is a low order expansion of the isotropic Schwarzschild metric. The procecure to get to the expression for the acceleration is a bit beyond me.

My question is:

What expression for the gravitational gravitation do you get if you use the anisotropic Schwarzschild metric and apply the same procedure?

I would also like to know why the isotropic Schwarzschild metric is used to derive an expression for the acceleration and not the anisotropic metric, which is more common in basic textbooks...

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# Anisotropic instead of isotropic metric deriving acceleration

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