Measuring the dimensionality of compact extra dimensions with inspiral gravitational waves from black-hole binaries

¹ Department of Geophysics, School of the Geology Engineering and Geomatics, Chang'an University Xi'an, 710064, China
² Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Beijing, 100190, China
³ Morningside Center of Mathematics, Chinese Academy of Sciences - Beijing, 100190, China

^(a) xupeng@amss.ac.cn

Received: 14 December 2016
Accepted: 12 January 2017

Abstract

Gravitational waves from coalescing black-hole binaries (BHBs) were recently observed by the advanced LIGO detectors. Based on the perturbation analysis, for general Kaluza-Klein theories with compact extra dimensions, we find a 1st-order post-Newtonian correction to the inspiral gravitational waveforms of black-hole binaries, that comes from the variations of the volume of the extra dimensions in near source zones. Such correction depends on a new parameter with n the dimensionality of the extra space and it is irrelevant to the particular choice of the topology of the extra space. For the ideal case of a black-hole binary system following nearly circular orbital motion with almost equal or intermediate mass ratio, such higher-dimensional corrections to the chirping amplitude are worked out. Giving the power of tracing inspiral waves from coalescing massive BHBs with high signal-to-noise ratios, the planned space-borne antennas such as the eLISA and DECIGO may give us a measurement of the parameter χ in the near future and may serve us as new probes in the searching for the evidence of the hidden compact dimensions.