Abstract
We consider the Einstein-Hilbert action without cosmological constant in 5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For non-zero compactification radius, the 4- dimensional spectrum contains massless and massive KK modes. For the massive KK modes, we retain four KK tensor and one KK scalar modes after a gauge fixing. We treat those massive KK modes as stochastic sources of gravitational wave (GW) with characteristic dependences of the frequencies on the size of the extra dimension. Using the observational bounds on the size of the extra dimension and on the characteristic strain, we make an order estimation on the frequencies and amplitudes of the massive KK modes that can contribute to the GW.
Highlights
The detection of gravitational waves (GWs) by the LIGO and Virgo Collaborations [1,2,3,4,5,6,7,8,9] from the merging of a pair of heavy black holes seems to be consistent with the prediction of Einstein’s general relativity
After general relativity was established, the idea to unify gravity and the electromagnetic force, known as the Kaluza-Klein (KK) reduction [12,13,14,15,16], was born. This was an innovative attempt based on the idea of the existence of extra dimensions, and later the presence of extra dimensions became an essential element in the study of unified theories, such as string or M-theories
We explicitly show that these massive modes contribute to metric fluctuations, which can have effects on the GW detections
Summary
The detection of gravitational waves (GWs) by the LIGO and Virgo Collaborations [1,2,3,4,5,6,7,8,9] from the merging of a pair of heavy black holes seems to be consistent with the prediction of Einstein’s general relativity. The massive KK modes, hI and h Iμν, behave as matter fields and play the role of the source for metric fluctuations in the equation of motion for the massless graviton h 0μν. From the various stochastic background GW observational limits [34,35,36,37,38,39,40], one can estimate the amplitude of the massive KK modes that corresponds to this minimum frequency
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