The claimed -1PN correction to the binary equations of motion is an artifact of an invalid expansion and never becomes larger than the Newtonian term, per the paper's own Eq. (97).
Gravity-wave detectors as probes of extra dimensions
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If string theory is correct, then our observable Universe may be a 3-dimensional "brane" embedded in a higher-dimensional spacetime. This theoretical scenario should be tested via the state-of-the-art in gravitational experiments -- the current and upcoming gravity-wave detectors. Indeed, the existence of extra dimensions leads to oscillations that leave a spectroscopic signature in the gravity-wave signal from black holes. The detectors that have been designed to confirm Einstein's prediction of gravity waves, can in principle also provide tests and constraints on string theory.
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Gravitational waves from a binary source in higher dimensional spacetime with compactified extra dimensions
The claimed -1PN correction to the binary equations of motion is an artifact of an invalid expansion and never becomes larger than the Newtonian term, per the paper's own Eq. (97).