
#1
Jan1912, 09:55 PM

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P: 1,716

I am wondering how space geographers would measure curvature of space around a large isolated star. i am thinking of the set up where there are two nearby spheres surrounding the star whose circumferences are already known. The remaining step is to measure the length of a radial geodesic segment connecting the two spheres. This it seems would give measurements in geodesic polar coordinates and would allow the computation of curvature using the usual formulas.
How then does one find a geodesic ray and the measure its length? 



#2
Jan1912, 11:23 PM

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PF Gold
P: 4,862

Aren't radial coordinate lines (t=theta=phi=0, SC coordinates) outside the horizon spacelike geodesics? It looks like this should be so from the geodesic equations, and it seems this is regularly assumed. Then you just integrated the line element along r, with all other coords held to zero.
Am I missing what you are asking? 



#3
Jan1912, 11:31 PM

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#4
Jan1912, 11:31 PM

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PF Gold
P: 4,862

measuring curvature of space around a star
Note, there are other more complex spacelike geodesics, but I assume those are not relevant.
Also, note that a free faller using GP coordinated can foliate a region of spacetime such that the spatial slices are exactly Euclidean flat for the induced metric. Then, all curvature would only be seen by involving time. 



#5
Jan1912, 11:34 PM

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PF Gold
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#6
Jan1912, 11:35 PM

P: 1,555

Closest to GP coordinates for a rotating star is the Doran metric. 



#7
Jan1912, 11:58 PM

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PF Gold
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#8
Jan2012, 12:25 AM

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#9
Jan2012, 12:45 AM

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PF Gold
P: 4,862

Of course, if you know the geometry, you could mathematically convert round trip light time to geodesic distance. You could use roundtrip light time * c as a radial distance coordinate directly. You just can't assume it measures proper distance. 


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