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Black Holes in a Gravitational Field: The Non-linear Static Love Number of Schwarzschild Black Holes Vanishes

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arxiv 2410.11014 v1 pith:YMUR2X3U submitted 2024-10-14 gr-qc hep-phhep-th

Alex Kehagias , Antonio Riotto This is my paper · ORCID
classification gr-qchep-phhep-th
keywords blackholesstaticlovenon-linearnumberschwarzschildtidal
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We show that the static tidal Love number of Schwarzschild black holes in four dimensions and in the vacuum vanishes at any order in the external tidal force. We also identify the underlying non-linear symmetry which is responsible for this result and becomes manifest when the black hole metric is written in axsymmetric static Weyl coordinates.

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Cited by 7 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. Perturbing Gravitational Atoms: Negative Love, Resonant Tides and Shifted Resonances

    gr-qc 2026-07 accept novelty 7.0 of 10

    Spinning gravitational atoms have negative static Love numbers enhanced by O(10²–10³) over non-spinning clouds, with internal perturbations shifting binary resonances.

  4. 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.

  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. 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.

  7. 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.

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