We extend the gravitational self-force approach to encompass "self-interaction" tidal effects for a compact body of mass μ on a quasicircular orbit around a black hole of mass M ≫ μ. Specifically, we define and calculate at OðμÞ (conservative) shifts in the eigenvalues of the electric-and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at OðμÞ. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order postNewtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves.
We extend the gravitational self-force methodology to identify and compute new O(µ) tidal invariants for a compact body of mass µ on a quasi-circular orbit about a black hole of mass M µ. In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative 'electric' invariants and 3+1 'magnetic' invariants, satisfying 1+1 and 1+0 trace conditions. We express the new invariants for equatorial circular orbits on Kerr spacetime in terms of the regularized metric perturbation and its derivatives; and we evaluate the expressions in the Schwarzschild case. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi. We present (i) highly-accurate numerical data and (ii) high-order analytical post-Newtonian expansions. We demonstrate consistency between numerical and analytical results, and prior work. We explore the application of these invariants in effective one-body models and binary black hole initial-data formulations.
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