ON INVARIANT QUALITATIVE CHAOS IN MULTI-BLACK-HOLE SPACETIMES

It is analytically shown when chaos exists in the behavior of null and timelike geodesics in the general case of geodesic motion in static a nd diagonal fields of general relativity. We demonstrate the effective ness of our method of investigating chaos in the behavior of geodesic motion in the multi-black-hole spacetimes. An optical model of chaotic behavior of geodesics in spacetimes with cylindrical symmetry is pres ented. The Lyapunov characteristic time is defined and estimated for g eodesic motion of a test particle in the external fields of general re lativity. We find that its value is positive in some compact regions o f the configuration space. This means that the trajectories have the p roperty of local instability which implies the sensitive dependence on initial conditions.