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One Membrane to Love them all: Tidal deformations of compact objects from the membrane paradigm
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One Membrane to Love them all: Tidal deformations of compact objects from the membrane paradigm
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The tidal deformability is a key observable to test the nature of compact objects in a binary coalescence. Within vacuum General Relativity, the tidal Love numbers of a four-dimensional black hole are strictly zero, while they are non-zero and model-dependent for material objects, matter distributions around black holes, or in alternative theories of gravity. Here, we develop a model-agnostic framework based on the membrane paradigm, where the tidal properties of a spherically symmetric object are encoded in the response of a fictitious membrane in terms of viscosity coefficients. We show that both neutron stars and exotic compact objects (in particular, we provide an explicit example for thin-shell gravastars) are included in this framework, provided that the bulk and shear viscosity coefficients of the membrane have a nontrivial frequency dependence. We derive a general result for the electric and magnetic tidal Love numbers for non-rotating and spherically symmetric compact objects in terms of the viscosity coefficients, discussing their behavior with the compactness of the object, and identifying the conditions for the logarithmic behavior found in previous literature for various ultracompact objects. Finally, we show that the membrane shear viscosity coefficients associated with neutron star models feature novel quasi-universal relations, which depend only mildly on the neutron-star equation of state.
Forward citations
Cited by 5 Pith papers
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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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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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Plunge spectra as discriminators of black hole mimickers
Plunge spectra of extreme mass ratio events onto black hole mimickers show a low-frequency resonance comb and a high-frequency deviation from black hole behavior above Mω_th ≈ 0.39.
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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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