% 168 words
\part{Geodesics in Schwarzschild space-time}
\label{sch}
\chapter{Introduction to geodesics in the Schwarzschild space-time}
In this part of the thesis we will give solutions for geodesic
orbits in the Schwarzschild space-time (black hole characterized
only by mass $M$), which is space-time with an event horizon at
\(r = 2M\). Solutions for time-like and null geodesics (except for
solution for $\tau$ and $t$ coordinates of non-radial geodesics)
are based on (and in greater detail explained in) \cite[Sections
19 and 20]{chandrasekhar}, while
space-like geodesics (sometimes associated with tachyons) are new.

\cite{hlr} claim there exist repulsive space-like orbits. Our
analysis in chapter~\ref{s} shows that because of restrictions
which have to be made on parameters $E$, $L$, and $M$, there are
only attractive space-like orbits in the Schwarzschild space-time.

Pictures of geodesics in this part were generated by {\sc Matlab}
(for source codes see appendix \ref{Matlab}) from differential
equations. %Because of the limits of numerical methods we took the
%liberty to extrapolate these orbits where it was obvious (mostly
%extensions of orbits into the singularity). These parts are cyan
%or gray to distinguish between computer generated orbits and their
%hand drawn extensions.
