Is There a Simple Explanation for the Area Element in Fermi Normal Coordinates?

[PLuz]

Hi everyone,

Defined the Fermi Normal Coordinates (which can be seen for example http://relativity.livingreviews.org/open?pubNo=lrr-2011-7&page=articlese10.html" ) is there any heuristic argument to explain why the area element is something proportional to the element of solid angle? I was trying to find a way to avoid the need to compute explicitly the area element in order prove for the first and third results of Eq.17.26 of that reference...

Any ideas?


Thank you

 

[clamtrox]

Surely it's because the 2 (or n? doesn't seem to matter)-sphere you're integrating over is a symmetric domain, and the integrand is always odd in at least one of the coordinates, so the integral has to vanish. The second result is the non-trivial one.