How much does a point mass curve spacetime at distance r?

[xortdsc]

Hello,

given a stationary pointlike particle with mass m at some position, I'm trying to compute just how much space is curved/deformed at a distance r from that particle due to its gravitational field.

I'm not really into all that tensor calculus, so I really struggle with the equations given in literature. I hope someone here can clear things up a little.

If I understood that whole SR/GR good enough I'd think it should be possible to compute a (3d vector) field, which in my particular case is still only dependent on the particles mass and the distance from it, which holds the "ratio" of spatial deformation compared to uncurved space (absence of any energy/mass which therefore would yield 1 everywhere).
I'm particularly interested in this ratio, which basically tells me how much space "scales" for each axis for an outside observer.

Thanks and cheers !

 

[A.T.]

I'm particularly interested in this ratio, which basically tells me how much space "scales" for each axis for an outside observer.

Sounds like you are asking about the spatial part of the Schwarzschild metric.
http://en.wikipedia.org/wiki/Schwarzschild_metric#The_Schwarzschild_metric

The ratio of proper radial distance to difference of circumferences divided by 2pi is (1 - r_s/r)^-1/2

 

[xortdsc]

Ah, so "sqrt(1-rs/r)" is simultaneously the time dilation ratio and space curvature ratio at distance r. Do I interpret this correctly ?