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Spinning Black Holes Fall in Love

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arxiv 2007.00214 v2 pith:H6C4Z76Q submitted 2020-07-01 gr-qc astro-ph.HEhep-th

Alexandre Le Tiec , Marc Casals This is my paper · ORCID
classification gr-qcastro-ph.HEhep-th
keywords blacklovetensorstidalholefieldholeskerr
verification ladder T0 review T1 audit T2 compute T3 formal

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The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics, astrophysics and gravitational-wave astronomy. Love tensors characterize the tidal deformability of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation. In contrast to this result, we show that Love tensors are generically nonzero for a spinning black hole. Specifically, to linear order in the Kerr black hole spin and the weak perturbing tidal field, we compute in closed form the Love tensors that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields. For a dimensionless spin ~ 0.1, the nonvanishing quadrupolar Love tensors are ~ 0.002, thus showing that black holes are particularly "rigid" compact objects.

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Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory

    hep-th 2025-12 accept novelty 8.0 of 10

    A shell-based EFT computes scalar Love numbers for Schwarzschild black holes through O(G^9) and conjectures an all-orders Riemann-zeta structure.

  2. Love numbers of black p-branes: fine tuning, Love symmetries, and their geometrization

    hep-th 2025-02 accept novelty 8.0 of 10

    Scalar Love numbers of non-dilatonic black p-branes vanish for integer rescaled multipoles, extremal p-branes give exactly zero static Love numbers, and the hidden symmetries behind these vanishings become near-horizo...

  3. A Bound on the Dynamical Love Number

    gr-qc 2026-07 conditional novelty 7.0 of 10

    Schwarz–Pick applied to the rescaled retarded tidal response bounds dynamical Love numbers for neutron stars by the static Love number and spectral gap, and constrains black-hole tidal heating.

  4. Dynamical Tidal Response of Schwarzschild Black Holes

    gr-qc 2025-11 conditional novelty 7.0 of 10

    The dynamical Love numbers of a Schwarzschild black hole are nonzero at quadratic order in frequency, run logarithmically with a coefficient set by dissipation, and are now matched including their finite, scheme-depen...

  5. One Membrane to Love them all: Tidal deformations of compact objects from the membrane paradigm

    gr-qc 2025-06 conditional novelty 7.0 of 10

    The tidal deformability of any compact object in vacuum general relativity can be encoded in the bulk and shear viscosity of a fictitious membrane, with explicit formulas for the electric and magnetic Love numbers.

  6. Running Love Numbers and the Effective Field Theory of Gravity

    hep-th 2025-01 conditional novelty 7.0 of 10

    Higher-derivative gravity corrections induce non-zero, classically running tidal Love numbers for black holes, computed here with a new tidal Green function method.

  7. Higher-Dimensional Black Holes and Effective Field Theory

    hep-th 2024-12 conditional novelty 7.0 of 10

    Higher-dimensional spinning black holes generally have nonzero scalar tidal Love numbers, with patterns of zeroes in special limits, computed via point-particle EFT matching.

  8. Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole

    gr-qc 2026-01 conditional novelty 6.0 of 10

    A closed-form Kerr metric under slow quadrupolar tides yields spin-dependent tidal shifts of the ISCO and light ring, with larger shifts for retrograde orbits around fast-spinning holes.

  9. On the logarithmic Love number of black holes beyond general relativity

    gr-qc 2025-12 conditional novelty 6.0 of 10

    Logarithmic black hole Love numbers are fixed directly by the Taylor coefficients of the perturbation equation, and perturbative deviations from Schwarzschild/Reissner-Nordström force non-zero running.

  10. The Vanishing of the Non-linear Static Love Number of Kerr Black Holes and the Role of Symmetries

    gr-qc 2024-12 conditional novelty 6.0 of 10

    Using the Ernst formalism, the paper argues that the static quadrupole tidal Love number of a Kerr black hole vanishes at full nonlinear order, because a decaying tidal mode would create a naked curvature singularity ...

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