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).
The treatment performed here is somewhat different from that in [21] and their results are also different
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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).