Asymptotic Behavior of Gravitational Waves on the Brane World

We consider the Cauchy problem of a gravitational wave with initial data distributed only around the brane in the one brane model of Randall and Sundrum and examine its asymptotic behavior inside the light cone on the brane as t -> ∞. We find its leading behavior is t^-6, unlike that of an ordinary flat 5-dimensional space-time. Such a result shows that the Huygens principle is violated on the 4-dimensional brane world even asymptotically and also shows the difference between compact and non-compact brane worlds. Some comments are also given related to AdS/CFT correspondence.