Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism

Abstract

Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal interactions (hitherto known only to the second post-Newtonian level) by extending our recently developed analytic self-force formalism, for extreme mass-ratio binary systems, to the computation of several tidal invariants. Specifically, we compute, to linear order in the mass ratio and to the 7.5${}^{\mathrm{th}}$ post-Newtonian order, the following tidal invariants: the square and the cube of the gravitoelectric quadrupolar tidal tensor, the square of the gravitomagnetic quadrupolar tidal tensor, and the square of the gravitoelectric octupolar tidal tensor. Our high-accuracy analytic results are compared to recent numerical self-force tidal data by Dolan et al. \cite{Dolan:2014pja}, and, notably, provide an analytic understanding of the light ring asymptotic behavior found by them. We transcribe our kinematical tidal-invariant results in the more dynamically significant effective one-body description of the tidal interaction energy. By combining, in a synergetic manner, analytical and numerical results, we provide simple, accurate analytic representations of the global, strong-field behavior of the gravitoelectric quadrupolar tidal factor. A striking finding is that the linear-in-mass-ratio piece in the latter tidal factor changes sign in the strong-field domain, to become negative (while its previously known second post-Newtonian approximant was always positive). We, however, argue that this will be more than compensated by a probable fast growth, in the strong-field domain, of the nonlinear-in-mass-ratio contributions in the tidal factor.

38 pages, 5 figures, revtex style

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• Tidal deformation of a slowly rotating black hole
• Effective-one-body multipolar waveform for tidally interacting binary neutron stars up to merger
• Evolution of small-mass-ratio binaries with a spinning secondary
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Tidal invariants for compact binaries on quasi-circular orbits
• Gravitomagnetic response of an irrotational body to an applied tidal field
• Exploring tidal effects of coalescing binary neutron stars in numerical relativity II: Longterm simulations
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Gravitational waveforms from SpEC simulations : neutron star-neutron star and low-mass black hole-neutron star binaries
• Updated universal relations for tidal deformabilities of neutron stars from phenomenological equations of state
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
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• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Gyroscope precession along bound equatorial plane orbits around a Kerr black hole
• Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• Gravitomagnetic tidal currents in rotating neutron stars
• Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary