The preprint of my latest paper with Patrick Nolan, Chris Kavanagh, Sam R Dolan, Adrian C Ottewill, and Niels Warburton is now available on the arXiv. The abstract for the article is below:

We extend the gravitational self-force methodology to identify and compute new tidal invariants for a compact body of mass on a quasi-circular orbit about a black hole of mass . 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. After formulating for equatorial circular orbits on Kerr spacetime, we calculate explicitly for Schwarzschild spacetime. 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 analytic results, and prior work. We explore the application of these invariants in effective one-body models, and binary black hole initial-data formulations, and conclude with a discussion of future work.

Update: The paper has now been published as Phys. Rev. D 92, 123008 (2015).