Patrick Nolan | Searcharxiv

arXiv2015

Octupolar invariants for compact binaries on quasi-circular orbits

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 $M \gg μ$. 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. 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.

gr-qc↗

arXiv2015

Tidal invariants for compact binaries on quasi-circular orbits

We extend the gravitational self-force approach to encompass `self-interaction' tidal effects for a compact body of mass $μ$ on a quasi-circular orbit around a black hole of mass $M \gg μ$. Specifically, we define and calculate at $O(μ)$ (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 $O(μ)$. 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 post-Newtonian 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.

gr-qc↗