We present an expression for the gravitational self-force correction to the geodetic spin precession of a spinning compact object with small, but non-negligible mass in a bound, equatorial orbit around a Kerr black hole. We consider only conservative backreaction effects due to the mass of the compact object ($m_1$), 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 mass parameter of the background Kerr spacetime. We encapsulate the correction to the spin precession in $\psi$, the ratio of the accumulated spin-precession angle to the total azimuthal angle over one radial orbit in the equatorial plane. Our formulation considers the gauge-invariant $\mathcal{O}(m_1)$ part of the correction to $\psi$, denoted by $\mathrm{\Delta }\psi$, and is a generalization of the results of Akcay et al. [Classical Quantum Gravity 34, 084001 (2017)] to Kerr spacetime. Additionally, we compute the zero-eccentricity limit of $\mathrm{\Delta }\psi$ and show that this quantity differs from the circular orbit $\mathrm{\Delta }{\psi }^{\text{circ}}$ by a gauge-invariant quantity containing the gravitational self-force correction to general relativistic periapsis advance in Kerr spacetime. Our result for $\mathrm{\Delta }\psi$ is expressed in a manner that readily accommodates numerical/analytical self-force computations, e.g., in the radiation gauge, and paves the way for the computation of a new eccentric-orbit Kerr gauge invariant beyond the generalized redshift.

• Received 9 June 2017

DOI:https://doi.org/10.1103/PhysRevD.96.044024