Okay, we have Einstein's field equation: R_ab + 1/2 R g_ab = 8pi T_ab Let's say we have T_ab defined for some region of space, and we want to calculate the spacetime from that. How would you calculate R_ab, R and g_ab? Supposedly you can write it as a system of PDEs but I cannot find them anywhere! I'm just starting to learn GR, if I could see how you'd put it in a computer to solve them it would help me "see" it better. Thanks.