Gravitational radiation from a binary system in odd-dimensional spacetime

TL;DR

This paper investigates gravitational radiation in odd-dimensional spacetimes, revealing unique features like a breathing mode and deriving a quadrupole-like formula in a simplified linearized model.

Contribution

It introduces an analytically solvable five-dimensional model to study gravitational radiation in odd dimensions, highlighting violations of Huygens' principle and new polarization modes.

Findings

Discovery of a breathing polarization mode in odd-dimensional gravitational waves.

Derivation of a quadrupole-like radiation formula with historical integral.

Identification of Huygens' principle violation effects in gravitational radiation.

Abstract

We explore possible manifestations of an odd number of extra dimensions in gravitational radiation, which are associated with violation of Huygens' principle in flat odd-dimensional spacetime. Our setup can be regarded as the limit of an infinite compactification radius in ADD model and is not viable as realistic cosmology, but it still may be useful as a simple analytically solvable model catching certain features of more realistic scenarios. The model consists of two point masses moving inside a flat three-dimensional brane, embedded in a five-dimensional Minkowski space and interacting only through a massless scalar field localized on the same brane, while gravitational radiation is emitted into the bulk. This setup avoids the difficulties associated with taking into account the gravitational stresses binding the system, which require the cubic terms in the perturbative gravitational Lagrangian, and permits to limit ourselves to linearized theory. We calculate radiation in a linearized five-dimensional gravity generalizing the Rohrlich-Teitelboim approach to extract the emitted part of the retarded gravitational field. The source term consists of a local contribution from point particles and a non-local contribution from scalar field stresses, which is calculated using the DIRE approach to post-Newtonian expansions. In the nonrelativistic limit, we find an analog of the quadrupole formula containing an integral over the history of the particles' motion preceding the retarded time. We also show that, for an observer on the brane, the radiation contains a third polarization: the breathing mode.