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Vanishing of black hole tidal Love numbers from scattering amplitudes

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arxiv 2209.14324 v1 pith:YG6TVIZF submitted 2022-09-28 hep-th astro-ph.HEgr-qchep-ph

Mikhail M. Ivanov , Zihan Zhou This is my paper · ORCID
classification hep-thastro-ph.HEgr-qchep-ph
keywords lovenumberstidalamplitudesblackeffectsfieldhigher
verification ladder T0 review T1 audit T2 compute T3 formal

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We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory (EFT) and in general relativity (GR). We point out that the GR amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational non-linearities in the wave region, whose proper treatment requires higher order EFT loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher dimensional BHs. Our results are manifestly gauge-invariant and coordinate-independent, thereby providing a valuable consistency check for the commonly used off-shell methods.

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Cited by 11 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. Matching Tidal Deformability (Wilson) Coefficients to Black Hole Love Numbers in Higher-Curvature Gravity

    gr-qc 2026-04 accept novelty 7.0 of 10

    Wilson coefficients in higher-curvature EFTs equal point-particle counterterms plus finite-size Love-number pieces; standard GR matching fails and is corrected for cubic gravity.

  4. Bouncing singularities and thermal correlators on line defects

    hep-th 2026-03 unverdicted novelty 7.0 of 10

    Retarded correlators of displacement operators on line defects in holographic thermal CFTs exhibit bouncing singularities that match between interior-sensitive WKB and boundary-only OPE analyses.

  5. 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...

  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. Spinning bodies in general relativity from bosonic worldline oscillators

    hep-th 2024-11 conditional novelty 7.0 of 10

    A bosonic-oscillator worldline action for spinning compact bodies in general relativity is constructed, and it reproduces known post-Minkowskian scattering results while remaining valid to all orders in spin.

  9. 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 ...

  10. Tidal deformation of an accreting compact object

    gr-qc 2026-07 conditional novelty 5.0 of 10

    For perfectly reflecting Schwarzschild-like ECOs, the log-compactness scaling of static scalar and spin-1 Love numbers survives a thin accretion disk, which mainly amplifies the response magnitude.

  11. Quantum Criticality in Black Hole Scattering

    hep-th 2024-11 reject novelty 4.0 of 10

    Kerr black hole scattering is reinterpreted as a quantum critical phenomenon, with a conformal critical point at extremality and the superradiant bound.

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