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Vanishing of Quadratic Love Numbers of Schwarzschild Black Holes
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The induced conservative tidal response of self-gravitating objects in general relativity is parametrized in terms of a set of coefficients, which are commonly referred to as Love numbers. For asymptotically-flat black holes in four spacetime dimensions, the Love numbers are notoriously zero in the static regime. In this work, we show that this result continues to hold upon inclusion of nonlinearities in the theory for Schwarzschild black holes. We first solve the quadratic Einstein equations in the static limit to all orders in the multipolar expansion, including both even and odd perturbations. We show that the second-order solutions take simple analytic expressions, generically expressible in the form of finite polynomials. We then define the quadratic Love numbers at the level of the point-particle effective field theory. By performing the matching with the full solution in general relativity, we show that quadratic Love number coefficients are zero to all orders in the derivative expansion, like the linear ones.
Forward citations
Cited by 4 Pith papers
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Multipolar static tidal response of Schwarzschild black holes in cubic gravity: a metric-action derivation of tidal running
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Perturbing Gravitational Atoms: Negative Love, Resonant Tides and Shifted Resonances
Spinning gravitational atoms have negative static Love numbers enhanced by O(10²–10³) over non-spinning clouds, with internal perturbations shifting binary resonances.
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Dynamical Tidal Response of Schwarzschild Black Holes
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...
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On the logarithmic Love number of black holes beyond general relativity
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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