Echoing the extra dimension

TL;DR

This paper investigates how gravitational waves can reveal the presence of extra dimensions by analyzing their propagation in a 5-dimensional spacetime with a compact extra dimension, highlighting unique effects and potential observational signatures.

Contribution

It derives the Green's function for gravitational wave propagation in a 5D spacetime with a compact extra dimension and identifies novel effects such as tail signals, screening, and frequency-dependent amplification.

Findings

Green's function expressed as a sum over images due to compact dimension

Discovery of tail effects and screening in wave signals

Potential for gravitational wave detectors to probe extra dimensions

Abstract

We study the propagating gravitational waves as a tool to probe the extra dimensions. In the set-up with one compact extra dimension and non-gravitational physics resigning on the 4-dimensional subspace (brane) of 5-dimensional spacetime we find the Green's function describing the propagation of 5-dimensional signal along the brane. The Green's function has a form of the sum of contributions from large number of images due to the compactness of the fifth dimension. Additionally, a peculiar feature of the causal wave propagation in five dimensions (making a five-dimensional spacetime very much different from the familiar four-dimensional case) is that the entire region inside the past light-cone contributes to the signal at the observation point. The 4-dimensional propagation law is nevertheless reproduced at large (compared to the size of extra dimension) intervals from the source as a superposition of signals from large number of images. The fifth dimension however shows up in the form of corrections to the purely 4-dimensional picture. We find three interesting effects: a tail effect for a signal of finite duration, screening at the forefront of this signal and a frequency-dependent amplification for a periodic signal. We discuss implications of these effects in the gravitational wave astronomy and estimate the sensitivity of gravitational antenna needed for detecting the extra dimension.