Gravitational waves in multi-dimensional theories

Presence of extra dimensions significantly modifies the gravitational wave signals from mergers of binary systems of compact objects. Of particular interest is the case of odd dimensions, where extraction of the emitted part of gravitational field is obscured by violation of the Huygens principle — odd-dimensional retarded Green’s functions are localised not only on the light cone, but also inside it. Therefore, the total retarded gravitational field of a localised source propagates in space with all velocities up to that of light, while its gravitational radiation must propagate exactly with the speed of light. This mismatch is resolved in the Rohrlich-Teitelboim approach to radiation. In this talk, we will consider a simplified model consisting of two particles moving inside a three-dimensional brane embedded in a five-dimensional spacetime, and interacting only through a massless scalar field localised on the same brane, while the gravitational radiation is emitted into a full five-dimensional bulk. In the limit of non-relativistic particles, we obtain a five-dimensional analog of the quadrupole formula for the gravitational radiation power, containing an integral over the history of the system’s motion preceding the retarded time. As a simple example, we will consider the gravitational radiation of a binary system on a circular orbit and the corresponding orbital evolution.