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.
