Asymptotic Behavior of Gravitational Wave on the Brane World

Abstract

We consider the Cauchy problem of the gravitational wave with the initial data distributed only around the brane in the one brane model of Randall and Sundrum, and examine its behavior as t\to\infty. Then we find its leading behavior is t^{-6} unlike an ordinary flat 5-dimensional space-time. Such a signal 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.