\section{The basic concepts}
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 {\em event\/}.
The trajectory of a body in space-time is called a {\em world line\/}.

The separation $ds$ between to infinitely close events with 
coordinates $(x^0,x^1,x^2,x^3)$ and $(x^0+dx^0,x^1+dx^1,x^2+dx^2,x^3+dx^3)$,
respectively, is given by
\be
ds^2 = g_{\mu\nu} dx^\mu dx^\nu,
\ee
where $g_{\mu\nu}$ is the {\em 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
\begin{displaymath}
ds^2 = \sum_{\mu=0}^3 \sum_{\nu=0}^3 g_{\mu\nu} dx^\mu dx^\nu.
\end{displaymath}

We can chose any coordinates we like.
For black holes, which a spherical symmetrical,
time + spherical polar coordinates, $(t,r,\theta,\varphi)$,
are well suited.
