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Analytical determination of the periastron advance in spinning binaries from self-force computations
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We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.
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Gauge-fixing for the completion problem of reconstructed metric perturbations of a Kerr spacetime
A two-condition gauge-fixing prescription determines the nonradiative gauge piece of Kerr metric perturbations for eccentric equatorial orbits.
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