Tidal invariants for compact binaries on quasi-circular orbits

Abstract

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

29 pages, 5 figures, 3 tables. Corrected data in Table I (cf arXiv:1409.6933) to match published version

References in corpus (13)

• Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16
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• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• Nonrotating black hole in a post-Newtonian tidal environment
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• A practical, covariant puncture for second-order self-force calculations
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
• Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• Observer-dependent tidal indicators in the Kerr spacetime

Cited by in corpus (15)

• Modeling the dynamics of tidally-interacting binary neutron stars up to merger
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• 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
• Self-Force Calculations with a Spinning Secondary
• Gravitomagnetic response of an irrotational body to an applied tidal field
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• 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