Love at First Loop: Quantum Deformability of Near-Extremal Black Holes
Abstract
The static Love numbers of black holes vanish in classical, four-dimensional, asymptotically flat General Relativity. We study how this changes for the response of near-extremal Reissner--Nordström black holes to a minimally coupled massless scalar, at energies where the Schwarzian mode of the near-horizon throat fluctuates strongly. The black hole then responds as a quantum system with a spectrum of states. Its static response is a polarizability, given by virtual transitions between them. For ℓ=0 the static Love number vanishes, by the shift symmetry of the scalar, but for multipoles ℓ≥1 the static Love numbers are nonzero: the finite rotational energy of the spin-ℓ intermediate states spoils the cancellation responsible for the classical result. Since the throat no longer has a classical geometry from which to read off a tidal response, we define it through the retarded Green's function, and compute its full frequency dependence at leading order in r+ω. Its conservative part requires renormalization: the near-horizon theory fixes the coefficient of its logarithm, and with it a dependence on the energy that no local term can remove, while its finite local terms are matching data of the four-dimensional theory. The dissipative part is finite and scheme independent. For ℓ≥1, it vanishes at low frequencies when the energy is below the rotational gap, while at the gap threshold it becomes non-analytic in frequency and produces a late-time t−3/2 tail.
Related
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BibTeX
@misc{cano2026love,
title = {{Love at First Loop: Quantum Deformability of Near-Extremal Black Holes}},
author = {Pablo A. Cano and Marina David and Roberto Emparan and Stefano Trezzi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17259},
eprint = {2610.17259},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17259},
}
RIS
TY - UNPB
TI - Love at First Loop: Quantum Deformability of Near-Extremal Black Holes
AU - Pablo A. Cano
AU - Marina David
AU - Roberto Emparan
AU - Stefano Trezzi
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17259
UR - https://arxiv.org/abs/2610.17259
AB - The static Love numbers of black holes vanish in classical, four-dimensional, asymptotically flat General Relativity. We study how this changes for the response of near-extremal Reissner--Nordström black holes to a minimally coupled massless scalar, at energies where the Schwarzian mode of the near-horizon throat fluctuates strongly. The black hole then responds as a quantum system with a spectrum of states. Its static response is a polarizability, given by virtual transitions between them. For ℓ=0 the static Love number vanishes, by the shift symmetry of the scalar, but for multipoles ℓ≥1 the static Love numbers are nonzero: the finite rotational energy of the spin-ℓ intermediate states spoils the cancellation responsible for the classical result. Since the throat no longer has a classical geometry from which to read off a tidal response, we define it through the retarded Green's function, and compute its full frequency dependence at leading order in r_+ω. Its conservative part requires renormalization: the near-horizon theory fixes the coefficient of its logarithm, and with it a dependence on the energy that no local term can remove, while its finite local terms are matching data of the four-dimensional theory. The dissipative part is finite and scheme independent. For ℓ≥1, it vanishes at low frequencies when the energy is below the rotational gap, while at the gap threshold it becomes non-analytic in frequency and produces a late-time t^−3/2 tail.
ER -