Coupled nonlinear partial differential equations or simple matrices?

[ilocar]

Why is it impossible to find ALL of einstein's equations in one place? well I suppose its irrelevant, I'd just like to know what math I have to do to define the energy-momentum tensor for a particle if I know say... its energy and momentum, or is that illegal? I'm struggling to grasp general relativity, from a mathematical standpoint; I get it philosophically, help please :(

 

[atyy]

In general relativity matter is modeled as different sorts of fields, not particles. It is these fields that have energy momentum tensors.

However, one can talk about a particle moving in curved spacetime as an approximation. In this approximation, spacetime curvature is produced by the energy-momentum tensors of all matter except for a particular particle. The particle then moves on the "background" curved spacetime created by all other matter.

http://relativity.livingreviews.org/Articles/lrr-2004-6/

 

[ilocar]

I may possibly be even more confused. the question I meant to ask was not how a particle moves but how do I take scalar values like energy and momentum and construct the matrix that defines the energy-momentum tensor, or is that something that only supercomputers, Einstein and Swartzchilde can do?