Geodesic Geometry of Black Holes

A geodesic is a curve that its tangent is
transported parallel with it. In this monograph it
is explained how geodesics are classified, described
methods of finding solutions of equations by which
geodesics are governed, and illustrated orbits
derived on the basis of these solutions. In this
book null, space-like and time-like geodesics are
studied in the case of the space-times of
Schwarzschild, Reissner-Nordstr"om and Kerr black
holes. A thorough treatment of the space-like
geodesics of the Schwarzschild solutions has been
given. These geodesics are the trajectories of
Tachyons (faster than light particles) and are
treated in a~complete manner. This has been done by
obtaining exact solutions and solving them
numerically. All solutions for geodesics for a
Reissner-Nordstr"om black hole have been given in
complete detail, i.e. time-like, null and space-like
geodesics and orbit of a charged particle.
Equatorial geodesics of all three types of the Kerr
black holes are considered ( slow Kerr , extreme
Kerr , and fast Kerr ), and few examples of orbits
out of equator are here, too.

Autorentext
Dr. Gabriela Slezakova has received her Masters from Masaryk University, Brno, Czech Republic in Physics, and PhD in Mathematics for Waikato University in Hamilton, New Zealand.

Klappentext
A geodesic is a curve that its tangent is transported parallel with it. In this monograph it is explained how geodesics are classified, described methods of finding solutions of equations by which geodesics are governed, and illustrated orbits derived on the basis of these solutions. In this book null, space-like and time-like geodesics are studied in the case of the space-times of Schwarzschild, Reissner-Nordstr"om and Kerr black holes. A thorough treatment of the space-like geodesics of the Schwarzschild solutions has been given. These geodesics are the trajectories of Tachyons (faster than light particles) and are treated in a~complete manner. This has been done by obtaining exact solutions and solving them numerically. All solutions for geodesics for a Reissner-Nordstr"om black hole have been given in complete detail, i.e. time-like, null and space-like geodesics and orbit of a charged particle. Equatorial geodesics of all three types of the Kerr black holes are considered ("slow Kerr" , "extreme Kerr", and "fast Kerr"), and few examples of orbits out of equator are here, too.