Running Love Numbers of Charged Black Holes

Lucas de Souza; Sergio Barbosa; Sylvain Fichet

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Running Love Numbers of Charged Black Holes

Sergio Barbosa, Sylvain Fichet, Lucas de Souza

High Energy Physics - Theory · Submitted 30 Jan 2026 · Published version

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The overall picture that emerges is that the QFT-induced tidal response of magnetic black holes saturates in the strong-field regime.

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Loops of virtual particles from the vacuum of quantum field theory (QFT) render black holes tidally deformable. We compute the static tidal response of unspinning charged black holes at arbitrary radius, using the perturbative formalism developed in 2501.18684. Since the gravitational and electromagnetic tidal responses mix, we generalize the notion of Love numbers to Love matrices. We derive the coupled equations of motion for the metric and electromagnetic fluctuations around purely electric and magnetic backgrounds. For large charged black holes, which are described by the Effective Field Theory (EFT) of gravity, we compute the full set of Love matrices induced by an arbitrary tower of $F^{2n}$ operators. We find that, although quantum corrections break electromagnetic duality, the Love matrices in electric and magnetic backgrounds are related by a $Z_2$ symmetry under electric-magnetic exchange. Going beyond EFT, we compute the Love matrices of small magnetic black holes. We show that the running of the Love matrices is governed by the running of the $U(1)$ gauge coupling, and we derive the correspondence between Love and $U(1)$ beta functions for arbitrary harmonics. The overall picture that emerges is that the QFT-induced tidal response of magnetic black holes saturates in the strong-field regime. These results imply that nearly-extremal magnetic black holes charged under an Abelian dark sector could be probed by gravitational-wave observations.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Loops of virtual particles from the vacuum of quantum field theory (QFT) render black holes tidally deformable.	background 1.00	0.08	0.05	asserted 1.00
s1	We compute the static tidal response of unspinning charged black holes at arbitrary radius, using the perturbative formalism developed in 2501.18684.	contribution 0.63	0.96	0.04	asserted 0.99
s2	Since the gravitational and electromagnetic tidal responses mix, we generalize the notion of Love numbers to Love matrices.	contribution 0.70	0.90	0.06	asserted 0.98
s3	We derive the coupled equations of motion for the metric and electromagnetic fluctuations around purely electric and magnetic backgrounds.	method 0.78	0.95	0.03	asserted 0.99
s4	For large charged black holes, which are described by the Effective Field Theory (EFT) of gravity, we compute the full set of Love matrices induced by an arbitrary tower of $F^{2n}$ operators.	contribution 0.95	0.96	0.10	asserted 1.00
s5	We find that, although quantum corrections break electromagnetic duality, the Love matrices in electric and magnetic backgrounds are related by a $Z_2$ symmetry under electric-magnetic exchange.	result 1.00	0.95	0.13	asserted 1.00
s6	Going beyond EFT, we compute the Love matrices of small magnetic black holes.	contribution 0.99	0.96	0.05	asserted 1.00
s7	We show that the running of the Love matrices is governed by the running of the $U(1)$ gauge coupling, and we derive the correspondence between Love and $U(1)$ beta functions for arbitrary harmonics.	result 0.97	0.96	0.30	asserted 1.00
s8	The overall picture that emerges is that the QFT-induced tidal response of magnetic black holes saturates in the strong-field regime.	result 0.77	0.84	0.36	asserted 0.99
s9	These results imply that nearly-extremal magnetic black holes charged under an Abelian dark sector could be probed by gravitational-wave observations.	interpretation 1.00	0.57	0.38	hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

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Original abstract

Loops of virtual particles from the vacuum of quantum field theory (QFT) render black holes tidally deformable. We compute the static tidal response of unspinning charged black holes at arbitrary radius, using the perturbative formalism developed in 2501.18684. Since the gravitational and electromagnetic tidal responses mix, we generalize the notion of Love numbers to Love matrices. We derive the coupled equations of motion for the metric and electromagnetic fluctuations around purely electric and magnetic backgrounds. For large charged black holes, which are described by the Effective Field Theory (EFT) of gravity, we compute the full set of Love matrices induced by an arbitrary tower of $F^{2n}$ operators. We find that, although quantum corrections break electromagnetic duality, the Love matrices in electric and magnetic backgrounds are related by a $Z_2$ symmetry under electric-magnetic exchange. Going beyond EFT, we compute the Love matrices of small magnetic black holes. We show that the running of the Love matrices is governed by the running of the $U(1)$ gauge coupling, and we derive the correspondence between Love and $U(1)$ beta functions for arbitrary harmonics. The overall picture that emerges is that the QFT-induced tidal response of magnetic black holes saturates in the strong-field regime. These results imply that nearly-extremal magnetic black holes charged under an Abelian dark sector could be probed by gravitational-wave observations.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Love at First Loop: Quantum Deformability of Near-Extremal Black Holes
hep-th 2026-10 accept novelty 7.0 of 10

Quantum effects from the Schwarzian mode produce non-zero static Love numbers for near-extremal Reissner-Nordström black holes for ℓ≥1, with running and threshold behavior.
Black Hole Love Numbers with Physics-Informed Neural Networks
gr-qc 2026-11 conditional novelty 6.0 of 10

A Sobolev-regularized physics-informed neural network with exact horizon boundary conditions reproduces static Kerr tidal Love numbers to 10^-5 accuracy without evaluating the Gamma-function connection formula.
The Love for Three Logarithms: Universal Running of Dynamical Love Numbers
hep-th 2026-10 conditional novelty 6.0 of 10

For any static, spherically symmetric black hole, the logarithmic running of dynamical Love numbers is encoded in one traceless 2x2 monodromy matrix with three entries A, B, C.
Perturbations of Charged Black Holes with Higher-Order Interactions
gr-qc 2026-09 conditional novelty 6.0 of 10

Charged black holes in the vector Horndeski non-minimal Maxwell theory are numerically stable across the pathology-free coupling range, and their ringdown spectra break parity isospectrality and electric-magnetic duality.
Tidal Response Beyond the Background Geometry in Einstein-Euler-Heisenberg Black Holes
gr-qc 2026-09 accept novelty 5.0 of 10

The quadrupolar logarithmic running matrix for Euler-Heisenberg charged black holes is (9aQ^2/10)[[0,-Q],[-Q,M]], with the second electromagnetic invariant contributing only through its quadratic fluctuations.

How the literature uses it

4 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Cites it as background 2 papers

Additional developments encompass finite-frequency effects [ref] , more general black hole backgrounds [ref] – most notably rotating (Kerr) black holes [ref] – as well as nonlinear tidal response coefficients [ref] .[For a comprehensive overview spanning both recent and past publications, see [ref] .]

Tidal Response and Thermodynamics of Black Holes · Introduction · 0.85
They have by now been found for time-dependent (dynamical) tides [ref] , in higher dimensions [ref] , in AdS backgrounds [ref] , for magnetically charged black holes [ref] , in modified gravity and for exotic compact objects [ref] , and in quantum-corrected spacetimes [ref] .

Extremal non-rotating black holes have no fermionic Love · Introduction · 0.85

What it cites · 115 sentences without a confident label

Builds on 2 papers

We review the analysis of [ref] and extend it to multiple tides.

Running Love Numbers and the Effective Field Theory of Gravity · Structure and Properties · 0.97
This section extends the analysis made in [ref] .

2503.20910 · Black Hole Properties from Dimensional Analysis · 1.00

Uses the method or tool of 2 papers

We compute the static tidal response of unspinning charged black holes at arbitrary radius, using the perturbative formalism developed in [ref] .

Running Love Numbers and the Effective Field Theory of Gravity · Introduction · 0.86
We decompose the $a_μ$ and $h_μν$ fluctuations into vector and tensor spherical harmonics on the two-sphere [ref] (see also [ref] ).

Static response and Love numbers of Schwarzschild black holes · Spherical Harmonics and Parity · 0.90

Compares with 3 papers

Consistently, the equation for $Ψ_h$ in the neutral limit reproduces the one from the Regge–Wheeler variable, (6.52) of [ref] .]

Running Love Numbers and the Effective Field Theory of Gravity · The Fluctuations of Electrically-Charged Black Holes · 0.90
Therefore, the transformed form of Eq. [ref] reads [equation] This result agrees with [ref] upon translating the conventions.

Love numbers and magnetic susceptibility of charged black holes · Leading-Order · 0.99
Therefore, the transformed form of Eq. [ref] reads [equation] This result agrees with [ref] upon translating the conventions.

Master equations for perturbations of generalised static black holes with charge in higher dimensions · Leading-Order · 0.99

Cites as support 1 paper

Therefore, extremal black holes of any size are dominated by the electromagnetic sector [ref] .

2503.20910 · Extremal Black Holes and Weak Gravity Conjecture · 0.96

Cites as background 69 papers

A general perturbative formula for the Love beta functions is derived in [ref] , and general considerations along these lines are also presented in [ref] .

Running Love Numbers and the Effective Field Theory of Gravity · Review: Black Holes as Point Particles · 0.80
A general perturbative formula for the Love beta functions is derived in [ref] , and general considerations along these lines are also presented in [ref] .

On the logarithmic Love number of black holes beyond general relativity · Review: Black Holes as Point Particles · 0.80
[The leading curvature corrections to neutral and charged black holes have been computed in [ref] . ] We consider purely electric or purely magnetic black holes, so that the invariant $F_μνF^μν$ vanishes.

Higher-order corrections to mass-charge relation of extremal black holes · Deformed Geometry in Weak-Field Regime · 0.84

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