In the theory of general relativity, gravity is treated as a curvature of
space-time instead of a force.
A point in the 4-dimensional space-time is called an *event*.
The trajectory of a body in space-time is called a *world line*.

The separation *ds* between to infinitely close events with
coordinates and ,
respectively, is given by

where is the *metric tensor*.
We use the Einstein summation convention: repeated indices are to be summed
over.
If we wrote the above equation with explicit summation, it would be

We can chose any coordinates we like. For black holes, which a spherical symmetrical, time + spherical polar coordinates, , are well suited.

Web Exhibition: Null Geodesics Around a Kerr Black Hole

Bo Milvang-Jensen (

Mon Jun 17 11:54:08 MDT 1996