1008.2650 (Sarbari Guha et al.)

Geodesic motions near a five-dimensional Reissner-Nordström Anti-de
Sitter black hole    [PDF]

Sarbari Guha, Pinaki Bhattacharya, Subenoy Chakraborty

In this paper, we have made a study of the geodesics of neutral particles
near a non-rotating, charged five-dimensional Reissner-Nordstr\"{o}m Anti-de
Sitter black hole from the point of view of effective potential formalism and
the dynamical systems approach. The horizons can be easily located from the
effective potential under which the test particles move. This also helps us to
study radial motion and to analyze the stability of radial trajectories. The
stability of circular orbits have also been analyzed and the radius of the
innermost stable circular orbits have been determined. Contrary to the case of
massive particles for which, in general, the circular orbits may have up to
eight possible values of specific radius, we find that the photons will only
have two distinct values for the specific radii of circular trajectories.
Finally we have used the dynamical systems analysis to determine the critical
points and the nature of the orbits for the timelike and null geodesics.

View original: http://arxiv.org/abs/1008.2650