Lorentz violation and red shift of gravitational waves in brane-worlds

In this paper we study the speed of gravitational waves in a brane world scenario and show that if the extra dimension is space-like, the speed of the propagation of such waves is greater in the bulk than that on the brane. Therefore, the 4D Lorentz invariance is broken in the gravitational sector. A comparison is also made between the red shift of such waves and those of the electromagnetic waves on the brane. Such a comparison is essential for extracting the signature of the extra dimension and thus clarifying the question of maximal velocity of gravitational waves in the bulk.