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).
Polchinski,String Theory: An Introduction to the Bosonic String(Cambridge University Press, 1998), ISBN 9780521633031
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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).