How can general relativity be used to calculate quantitative answers?

[mt8891]

I was just curious as to how someone could find a Quantitative answer out of the equations for general relativity. I've tried to mess around with stuff related to tensors and manifolds but yeah, I can only compute so much given my foundation. In an attempt to build and forge that foundation I try and obtain some answers. My one question was how did Einstein calculate red shift and that sort of deal. Also, how could someone obtain any quantitative answers to any sort of problem.

For instance. what if there were two bodies of mass in some distant corner of the universe. Each was of a different but significant difference in mass. What would be the amount that the light would bend if it were traveling between the two bodies.

 

[Mentz114]

First you need to choose a spacetime that represents the situation you are modelling. For instance a universe filled sparsly with matter, which is homogenous and isotropic ( ie pretty much the same everywhere with no preferred directions) can be modeled using the FLRW metric ( Friedmann-LeMaitre-Robertson-Walker ) see
http://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric.

Using this model it is possible to put numbers on the energy density of the universe, using the observed rate of expansion. Look up 'Cosmological redshift' for the answer to your final question.

 

[Passionflower]

For instance. what if there were two bodies of mass in some distant corner of the universe. Each was of a different but significant difference in mass. What would be the amount that the light would bend if it were traveling between the two bodies.

The way GR works is that the whole shape of spacetime has to be encoded. One cannot add up different elements as superposition does not work because the theory is non-linear.

An additional issue is that the field equations have many solutions for a particular metric and it is not necessarily trivial to determine which solution makes any physical sense.

Another issues is that apart from the simplest spacetimes one need to describe the initial values of the problem one wants to analyze.

Thus a seemingly simple problem with two masses is far from trivial.