How would you calculate how bodies curve space/time?

In summary, the Swarzchild metric is a solution to Einstein's field equations and can be used to calculate the curvature of space-time around a non-rotating, non-charged black hole. It is not a simple concept and requires a deeper understanding of general relativity to fully comprehend.
  • #1
zeromodz
246
0
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.
 
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  • #2
zeromodz said:
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
 
  • #3
zeromodz said:
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.
 
  • #4
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
 
  • #5
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.
 

Related to How would you calculate how bodies curve space/time?

1. How does mass affect the curvature of space/time?

According to Einstein's theory of general relativity, mass and energy are the source of gravitational fields that curve space and time. The more massive an object is, the more it curves the space/time around it.

2. Can you provide an equation for calculating the curvature of space/time?

The equation for calculating the curvature of space/time is called the Einstein field equations. It involves the energy-momentum tensor, which represents the distribution of matter and energy in space, and the Einstein tensor, which describes the curvature of space/time.

3. Does the speed of an object affect the curvature of space/time?

According to general relativity, an object's speed does not directly affect the curvature of space/time. However, the energy and momentum of an object do contribute to the curvature, and these are related to an object's speed through Einstein's famous equation E=mc^2.

4. How do you account for the curvature of space/time in the presence of multiple massive objects?

In the presence of multiple massive objects, the curvature of space/time is calculated by adding the contributions of each object's energy and momentum. This can get very complex, but Einstein's field equations can handle these calculations.

5. Is it possible to measure the curvature of space/time?

Yes, it is possible to measure the curvature of space/time through various experiments and observations. One famous example is the bending of starlight around the sun during a solar eclipse, which confirmed Einstein's theory of general relativity and the curvature of space/time.

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