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Addressing issues in defining the Love numbers for black holes
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Addressing issues in defining the Love numbers for black holes
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We present an analytic method for calculating the tidal response function of a nonrotating and a slowly rotating black hole from the Teukolsky equation in the small-frequency and near horizon limit. We point out that in the relativistic context, there can be two possible definitions of the tidal Love numbers and the dissipative part that arises from the tidal response function. Our results suggest that both of these definitions predict zero tidal Love numbers for a nonrotating black hole. On the other hand, for a slowly rotating black hole in a generic tidal environment, these two definitions of the tidal Love numbers do not coincide. While one procedure suggests zero tidal Love numbers, the other procedure gives purely imaginary tidal Love numbers. As expected, the dissipative terms differ as well. We emphasize that in our analysis, we keep all the terms linear in the frequency, unlike previous works in the literature. Following this, we propose a procedure to calculate the tidal response function -- and hence the Love numbers -- for an arbitrarily rotating black hole.
Forward citations
Cited by 7 Pith papers
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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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Fermionic Love number of higher-dimensional Reissner-Nordstr\"om black holes
Fermionic tidal Love numbers for D-dimensional RN black holes remain nonzero for all angular momentum l (except extremal cases) and lose their l-dependence as D grows to infinity.
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Fermionic Love number of Reissner-Nordstr\"om black holes
Static fermionic tidal Love numbers are non-vanishing for non-extremal Reissner-Nordström black holes.
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Tidal deformation of an accreting compact object
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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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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