How would you calculate how bodies curve space/time?

[zeromodz]

Okay, I am really interested in relativity, but very ignorant in it also. I already know you would divide regular space/time by

√(1 - rs/r)

rs = schwarzschilds radius
r = radius of object from center of mass

How would we define regular space/time in an equation? What units or dimensions do we get the answer in. Thanks in advanced for answering.

 

[A.T.]

Okay, I am really interested in relativity, but very ignorant in it also. I already know you would divide regular space/time by

√(1 - rs/r)

rs = schwarzschilds radius
r = radius of object from center of mass

How would we define regular space/time in an equation? What units or dimensions do we get the answer in. Thanks in advanced for answering.

Look at:
http://en.wikipedia.org/wiki/Schwarzschild_metric

Here some visualizations of it:
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf

 

[Jonathan Scott]

Okay, I am really interested in relativity, but very ignorant in it also. I already know you would divide regular space/time by

√(1 - rs/r)

rs = schwarzschilds radius
r = radius of object from center of mass

How would we define regular space/time in an equation? What units or dimensions do we get the answer in. Thanks in advanced for answering.

If you don't need to handle really strong fields, you can just use the approximation that the curvature is 1/R = g/c² where g is the Newtonian acceleration. That value gives the effective acceleration g = c²/R for something at rest, and also gives the curvature of space, so that if the speed is v perpendicularly to the field there is an extra acceleration of v²/R, and if v=c the total acceleration is twice the Newtonian value.

 

[Matterwave]

You calculate how matter/energy curve space-time by solving the Einstein Field Equations.

The Swarzchild metric is one exact solution (the first one that was found! Other than the normal flat metric (or sometimes called the Minkowski space)) to Einstein's field equations. This solution is valid for non-rotating, non-charged, black holes (basically the space around a spherical object that just sits there). There are others, such as the Kerr metric for a rotating black hole. And there are even others where the space is not "empty" such as for these solutions, and therefore the stress-energy tensor is non-zero (I'm not sure if we've found any exact solutions to those).

http://en.wikipedia.org/wiki/Einstein_field_equation

 

[bcrowell]

Zeromodz, this is not a simple question with a simple answer. It's not the kind of thing where people can just give you a couple of formulas and then you'll be all set. You might want to start by reading a good elementary description of general relativity, such as the one in Hewitt's Conceptual Physics, or Relativity Simply Explained by Gardner.