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Revisiting the matching of black hole tidal responses: a systematic study of relativistic and logarithmic corrections
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Revisiting the matching of black hole tidal responses: a systematic study of relativistic and logarithmic corrections
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The worldline effective field theory (EFT) gives a gauge-invariant definition of black hole conservative tidal responses (Love numbers), dissipation numbers, and their spin-0 and spin-1 analogs. In the first part of this paper we show how the EFT allows us to circumvent the source/response ambiguity without having to use the analytic continuation prescription. The source/response ambiguity appears if Post-Newtonian (PN)corrections to external sources overlap with the response. However, these PN corrections can be clearly identified and isolated using the EFT. We illustrate that by computing static one-point functions of various external fields perturbing the four-dimensional Schwarzschild geometry. Upon resumming all relevant Feynman diagrams, we find that the PN terms that may mimic the response actually vanish for static black holes. Thus, the extraction of Love numbers from matching the EFT and general relativity (GR) calculations is completely unambiguous, and it implies that the Love numbers vanish identically for all types of perturbations. We also study in detail another type of fine tuning in the EFT, the absence of Love numbers' running. We show that logarithmic corrections to Love numbers do stem from individual loop diagrams in generic gauges, but cancel after all diagrams are summed over. In the particular cases of spin-0 and spin-2 fields the logarithms are completely absent if one uses the Kaluza-Klein metric decomposition. In the second part of the paper we compute frequency-dependent dissipative response contributions to the one-point functions using the Schwinger-Keldysh formalism. We extract black hole dissipation numbers by comparing the one-point functions in the EFT and GR. Our results are in perfect agreement with those obtained from a manifestly gauge-invariant matching of absorption cross-sections.
Forward citations
Cited by 9 Pith papers
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Universal Closed Form for Dynamical Love Numbers of Black Holes
Derives a universal closed-form expression for the dynamical response of Schwarzschild black holes using RG resummation and far-zone matching, verified via shell EFT to high orders.
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A Bound on the Dynamical Love Number
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.
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Axial tidal Love numbers of black holes in matter environments
Axial tidal Love numbers for black holes in anisotropic fluid environments are derived analytically and numerically, with non-compact support density profiles producing logarithmic terms that obstruct standard tidal m...
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Dynamical tidal Love numbers of black holes under generic perturbations: Connecting black hole perturbation theory with effective field theory
Dynamical tidal Love numbers for Kerr black holes are obtained to linear frequency order by matching EFT worldline couplings to black-hole perturbation solutions, including spin-induced mode mixing.
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Matching Tidal Deformability (Wilson) Coefficients to Black Hole Love Numbers in Higher-Curvature Gravity
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.
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5-Dimensional Gravitational Raman Scattering: Scalar Wave Perturbations in Schwarzschild-Tangherlini Spacetime
Derives closed 5D partial-wave Raman scattering amplitude via NS functions and computes non-vanishing dynamical ℓ=0 and static ℓ=1 scalar tidal Love numbers with RG running up to O(G²) for STBH.
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Tidal Response and Thermodynamics of Black Holes
A new gauge-invariant effective action computes black hole Love numbers without Regge-Wheeler methods, and these numbers determine leading thermodynamic corrections under external perturbations.
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Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
Renormalized dynamical tidal response functions for non-rotating black holes in GR carry inevitable ambiguities from renormalization scheme and flow initial condition, yielding scheme-dependent dynamical tidal Love nu...
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Universal Ladder Structure Across Scales: From Quantum to Black Hole Physics
A symmetry-based litmus test identifies when physical systems governed by second-order ODEs possess ladder structures and constructs them, linking supersymmetric quantum mechanics to Kerr black-hole tidal responses.
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