Christmas is the season for mathematics

Continuing what sadly enough was a Boxing Day discussion of gravity, here's a primer on the Einstein Gravitational Field Equations.

Field Equation

This elegant symbolic formulation of Einstein's general theory of relativity cannot be used for actual calculations, but it clearly shows the principle that "matter tells spacetime how to curve, and curved space tells matter how to move"(John Wheeler, Princeton University and the University of Texas at Austin). The left side of the equation contains all the information about how space is curved, and the right side contains all the information about the location and motion of the matter. General relativity is beautiful and simple (to a physicist), but mathematically it's very complicated and subtle.

If you understood all that, then check out the 2-D expansion of the tensor form of the equations. And if that wasn't fun enough, grab yourself a copy of f2c (and gcc) and admire the 3-D representation of the equations in FORTRAN!

Or just check a pictogram if this is getting a little math-y for your tastes.