Analytical determination of the periastron advance in spinning binaries from self-force computations

Understand

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.