Tidal invariants for compact binaries on quasicircular orbits

Sam R. Dolan, Patrick Nolan, Adrian C. Ottewill, Niels Warburton, and Barry Wardell
Phys. Rev. D 91, 023009 – Published 23 January 2015

Abstract

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 Mμ. 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.

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  • Received 20 August 2014

DOI:https://doi.org/10.1103/PhysRevD.91.023009

© 2015 American Physical Society

Authors & Affiliations

Sam R. Dolan1,*, Patrick Nolan2, Adrian C. Ottewill2, Niels Warburton2, and Barry Wardell3

  • 1Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom
  • 2School of Mathematical Sciences and Complex & Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland
  • 3Department of Astronomy, Cornell University, Ithaca, New York 14853, USA

  • *s.dolan@sheffield.ac.uk

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Vol. 91, Iss. 2 — 15 January 2015

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