Relativistic theory of tidal Love numbers

By T. Binnington, E. Poisson. 2009

481 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c0df845f8b3afd88aadd188c99c324dfad93c7d6

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In Astronomy and Astrophysics

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In Statistical and Nonlinear Physics

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Citations in the corpus

• The tune of love and the nature(ness) of spacetime (2016, background): “Following the electromagnetic example, the response to an external field can be written as follows (at leading order in spatial derivatives) [16, 17, 32, 33]”
• Static response and Love numbers of Schwarzschild black holes (2020, methodology): “In four dimensions, Schwarzschild black hole Love numbers were computed by [42, 43], while in higher dimensions they were computed for scalar-type and tensor-type perturbations in [45, 48].”
• The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “It turns out the (renormalized) CE(B) vanish for black holes in four spacetime dimensions [196, 197, 219].”
• Black hole perturbation theory and gravitational self-force (2021, background): “But note that the quadrupole moments of compact objects differ primarily due to their differing tidal deformability, and this difference is suppressed by an additional five powers of ε [23], suggesting it is almost certainly irrelevant for small-mass-ratio binaries.”
• Superradiance (2015, background): “y relevant dissipation time scale in the BH case is the light-crossing time ˝˘M, Eq. (3.68) was found to agree [135] with the exact result for BH tidal heating obtained through BH perturbation theory [138,139,140,141,142]. 30 4 Superradiance in black hole physics As discussed in the previous section”
• Approximate Universal Relations for Neutron Stars and Quark Stars (2016, methodology): “In practice, the calculation of the tidal deformation is similar to solving the perturbed Einstein equations in the slow-rotation approximation, except that here one sets the odd-parity (rotation-related) perturbations to zero and does not impose asymptotic flatness [27, 28, 154].”
• Superradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics (2015, unknown): “67) was found to agree [135] with the exact result for BH tidal heating obtained through BH perturbation theory [138, 139, 140, 141, 142].”