Relativistic theory of tidal Love numbers

Taylor Binnington and Eric Poisson
Phys. Rev. D 80, 084018 – Published 14 October 2009

Abstract

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body’s internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

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  • Received 7 June 2009

DOI:https://doi.org/10.1103/PhysRevD.80.084018

©2009 American Physical Society

Authors & Affiliations

Taylor Binnington

  • Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada

Eric Poisson

  • Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada; and Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, M5S 3H8, Canada

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Vol. 80, Iss. 8 — 15 October 2009

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