Probing Compactified Extra Dimensions with Gravitational Waves. (arXiv:2004.03051v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Du_Y/0/1/0/all/0/1">Yuchen Du</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Tahura_S/0/1/0/all/0/1">Shammi Tahura</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Vaman_D/0/1/0/all/0/1">Diana Vaman</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Yagi_K/0/1/0/all/0/1">Kent Yagi</a>

We study the effect of compact extra dimensions on the gravitational wave
luminosity and waveform. We consider a toy model, with a compactified fifth
dimension, and matter confined on a brane. We work in the context of five
dimensional ($5d$) general relativity, though we do make connections with the
corresponding Kaluza-Klein effective $4d$ theory. We show that the luminosity
of gravitational waves emitted in $5d$ gravity by a binary with the same
characteristics (same masses and separation distance) as a $4d$ binary is
20.8% less relative to the $4d$ case, to leading post-Newtonian order. The
phase of the gravitational waveform differs by 26% relative to the $4d$ case,
to leading post-Newtonian order. Such a correction arises mainly due to the
coupling between matter and dilaton field in the effective $4d$ picture and
agrees with previous calculations when we set black holes’ scalar charges to be
those computed from the Kaluza-Klein reduction. The above correction is
inconsistent with the recent gravitational-wave observations and it thus
effectively rules out the possibility of such a simple compactified higher
dimensions scenario. We also comment on how our results change if there are
several compactified extra dimensions, and show that the discrepancy with $4d$
general relativity only increases.

We study the effect of compact extra dimensions on the gravitational wave
luminosity and waveform. We consider a toy model, with a compactified fifth
dimension, and matter confined on a brane. We work in the context of five
dimensional ($5d$) general relativity, though we do make connections with the
corresponding Kaluza-Klein effective $4d$ theory. We show that the luminosity
of gravitational waves emitted in $5d$ gravity by a binary with the same
characteristics (same masses and separation distance) as a $4d$ binary is
20.8% less relative to the $4d$ case, to leading post-Newtonian order. The
phase of the gravitational waveform differs by 26% relative to the $4d$ case,
to leading post-Newtonian order. Such a correction arises mainly due to the
coupling between matter and dilaton field in the effective $4d$ picture and
agrees with previous calculations when we set black holes’ scalar charges to be
those computed from the Kaluza-Klein reduction. The above correction is
inconsistent with the recent gravitational-wave observations and it thus
effectively rules out the possibility of such a simple compactified higher
dimensions scenario. We also comment on how our results change if there are
several compactified extra dimensions, and show that the discrepancy with $4d$
general relativity only increases.

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