## Appendix A:The Lyapunov characteristic exponent of two nearby trajectories, and , is defined by where is a solution of the
equations of motion in the phase space,
is a connecting vector,
is its length in the phase space
and is an initial separation (the
value of must be small; otherwise
it is arbitrary and one usually scales
to unity). The Kerr spacetime being
stationary, we can measure the separations on the
surfaces. One defines
as the maximum value of
with respect to variations of
The maximum Lyapunov characteristic exponent is frequently
determined numerically. This approach requires a careful choice of the
integration scheme. In order to keep computational errors under
control, one lets the trajectories evolve for a short interval of
time, , after which independently of the value of In addition, for almost all Again, one can conveniently set . © European Southern Observatory (ESO) 1999 Online publication: March 1, 1999 |