How can the Riemann tensor help me calculate the bend in space-time?

[Kaleetos]

Hi. Could anyone here help/teach me how to calculate the resulting bend in space-time from any particular mass? Specifically I'm trying to figure out how much space-time is stretched or bent relative to "unbent" space-time in space. I'm not exactly sure this is the right question to be asking even, but if anyone could point me to the right formulas that would be very helpful. Thanks!

 

[Kaleetos]

One more question: How do you calculate the acceleration due to gravity from different distances from the center of the earth. I know g is constant for thing close to the surface of the earth-- but how do I find the acceleration due to gravity for things in different layers of the atmosphere?

 

[A.T.]

Hi. Could anyone here help/teach me how to calculate the resulting bend in space-time from any particular mass?

For spherical masses you would take the Schwarzshild-Metric
http://en.wikipedia.org/wiki/Schwarzschild_metric

One more question: How do you calculate the acceleration due to gravity from different distances from the center of the earth.

You mean in Genetal Relativity? Its Eq. 8 in this paper:
http://articles.adsabs.harvard.edu//full/1975AN...296..109T/0000109.000.html
Or in Newtonian mechanics? :
g = gravitational_constant * mass_of_earth / distance_from_center_of_the_earth^2

 

[pmb_phy]

Hi. Could anyone here help/teach me how to calculate the resulting bend in space-time from any particular mass? Specifically I'm trying to figure out how much space-time is stretched or bent relative to "unbent" space-time in space. I'm not exactly sure this is the right question to be asking even, but if anyone could point me to the right formulas that would be very helpful. Thanks!

The curvature of spacetime is described by the Riemann tensor. I recommend that you do a web search on that term.

Best wishes

Pete