Probing extra dimension through gravitational wave observations of compact binaries and their electromagnetic counterparts

TL;DR

This paper explores how gravitational wave and electromagnetic signals from compact binaries can be used to detect extra dimensions by analyzing their different propagation behaviors in a five-dimensional anti-de Sitter space-time.

Contribution

It introduces a novel method to probe extra dimensions by comparing the propagation horizons of GWs and EMWs in curved five-dimensional space-time models.

Findings

GW horizon radius exceeds EMW horizon radius in general cases.

Curvature parameters significantly influence the propagation horizons.

Method applied to GW150914 and X-ray events to illustrate potential for extra dimension detection.

Abstract

The future gravitational wave (GW) observations of compact binaries and their possible electromagnetic counterparts may be used to probe the nature of the extra dimension. It is widely accepted that gravitons and photons are the only two completely confirmed objects that can travel along null geodesics in our four-dimensional space-time. However, if there exist extra dimensions and only GWs can propagate freely in the bulk, the causal propagations of GWs and electromagnetic waves (EMWs) are in general different. In this paper, we study null geodesics of GWs and EMWs in a five-dimensional anti-de Sitter space-time in the presence of the curvature of the universe. We show that for general cases the horizon radius of GW is longer than EMW within equal time. Taking the GW150914 event detected by the Advanced Laser Interferometer Gravitational-Wave Observatory and the X-ray event detected by the Fermi Gamma-ray Burst Monitor as an example, we study how the curvature $k$ and the constant curvature radius $l$ affect the horizon radii of GW and EMW in the de Sitter and Einstein-de Sitter models of the universe. This provides an alternative method for probing extra dimension through future GW observations of compact binaries and their electromagnetic counterparts.