Asymptotic Behavior of Gravitational Wave on the Brane World

TL;DR

This paper analyzes the long-term behavior of gravitational waves in a brane world model, revealing a decay rate different from flat space and implications for the Huygens principle and AdS/CFT correspondence.

Contribution

It demonstrates the asymptotic decay rate of gravitational waves on the brane and shows the violation of the Huygens principle in this context.

Findings

Gravitational wave amplitude decays as t^{-6}

Huygens principle is violated asymptotically

Differences between compact and non-compact brane worlds

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.