% 179 words
\chapter{Summary of Part~\ref{r-n}}
The main difference between geodesics in Schwarzschild and
Reissner-Nordstr\"om solutions comes from the function f$(u)$,
which is, in the Schwarzschild black hole, cubical, and in the
Reissner-Nordstr\"om black hole, quartic. That means that, while
orbits of the first kind (bound or unbound) look essentially the
same, orbits of the second kind fall into the singularity of the
Schwarzschild black hole, unlike in the case of the
Reissner-Nordsr\"om black hole, where they end at some finite
distance from the singularity.

Again there are similarities between null, space-like and
time-like unbound geodesics in the Reissner-Nordstr\"om space-time
(all of them are unbounded), and, as before, only time-like
geodesics can be bound.

Radius of a circular orbit depends on relation of black hole
parameters $M$ and $Q_*$. To see how charge of a black hole
affects the circular orbit one may look at time-like geodesic in
Schwarzschild space-time, where circular orbits have radius $r
\geq 3M$, and compare it with circular geodesic in
Reissner-Nordstr\"om space-time, which have radius $r \geq \frac
32M(1 + \sqrt{1-\frac{8Q_*^2}{9M^2}})$ when $M^2 \geq Q_*^2$, and
$r \geq Q_*^2/M$ otherwise.

The solution for charged particles are formally the same as the
solution for time-like geodesics, however the conditions for
existence of circular orbits differ. Since there is one more
parameter to consider ($q$ -- charge of the particle), discussion
of the occurrence of different cases is not trivial. We expect the
orbits of charged particles to look the same as those that are not
charged, with the addition of repulsive orbits when $qQ_*
> 0$.

The main contribution of the thesis is in providing general
solutions of the time-like and the null geodesics as opposed to
special circular orbits which can be found in
\cite{chandrasekhar}, and discussion of the space-like geodesics.
All three types of geodesics are considered for black holes with
$M > |Q_*|$ as well as $M \leq |Q_*|$.

In Chapter \ref{rncharge} the solutions for orbits of the charged
particles are given, extending the prior work of \cite{chandrasekhar}.





