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We present an expression for the gravitational self-force correction to thegeodetic spin precession of a spinning compact object with small, butnon-negligible mass in a bound, equatorial orbit around a Kerr black hole. Weconsider only conservative back-reaction effects due to the mass of the compactobject ($m_1$) thus neglecting the effects of its spin $s_1$ on its motion,i.e, we impose $s_1 \ll G m_1^2/c$ and $m_1 \ll m_2$, where $m_2$ is the massparameter of the background Kerr spacetime. We encapsulate the correction tothe spin precession in $\psi$, the ratio of the accumulated spin-precessionangle to the total azimuthal angle over one radial orbit in the equatorialplane. Our formulation considers the gauge-invariant $\ord(m_1)$ part of thecorrection to $\psi$, denoted by $\Delta\psi$, and is a generalization of theresults of [Class. Quan. Grav., 34, 084001 (2017)] to Kerr spacetime.Additionally, we compute the zero-eccentricity limit of $\Delta\psi$ and showthat this quantity differs from the circular-orbit $\Delta\psi^\text{circ}$ bya gauge-invariant quantity containing the gravitational self-force correctionto general relativistic periapsis advance in Kerr spacetime. Our result for$\Delta\psi$ is expressed in a manner that readily accommodatesnumerical/analytical self-force computations, e.g., in radiation gauge, andpaves the way for the computation of a new eccentric-orbit Kerr gauge invariantbeyond the generalized redshift.

Self-force correction to geodetic spin precession in Kerr spacetime