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Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes

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arxiv 2312.05065 v2 pith:U5C3U473 submitted 2023-12-08 gr-qc hep-th

Massimiliano Maria Riva , Luca Santoni , Nikola Savić , Filippo Vernizzi This is my paper
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keywords loveorderschwarzschildtidalblackholeslinearnonlinear
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It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.

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Cited by 5 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. Multipolar static tidal response of Schwarzschild black holes in cubic gravity: a metric-action derivation of tidal running

    gr-qc 2026-08 conditional novelty 7.0 of 10

    In cubic Weyl gravity, the metric-field derivation reproduces the known canonical electric beta functions, proves the quadrupole is the unique non-running electric multipole via an L-6 source factor, and gives explici...

  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. 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. 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.

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