Quasinormal-mode stability bounds in gravitational EFT: resolvability, predictivity, and positivity
Abstract
It has been proposed that consistency limits how slowly black holes can ring down in extensions of General Relativity: effective-field-theory (EFT) corrections may lengthen the decay time of a quasinormal mode by at most about one oscillation period, ℜ[ωGR] δτ≲1. We argue that, under standard power counting, this condition yields no new, model-independent constraint on gravitational EFTs. First, its motivation does not extend straightforwardly to black holes: the inverse oscillation frequency is not a universal, detector-independent uncertainty in the damping time of a classical waveform. Our main argument, however, rests on eikonal power counting alone. The decay-time shift grows with the angular momentum ℓ of the mode, but so does the weight of higher-derivative operators. When curvature and derivatives are controlled by a single scale Λ, as in every known ultraviolet completion, the EFT around a black hole of radius rs remains predictive up to ℓ∼(rsΛ)2, and the shift becomes of order one only there, where an infinite tower of operators contributes at the same order. A resolvable shift within the predictive regime requires either large numerical coefficients or a two-scale power counting, which has no known ultraviolet completion. In both cases the quartic-curvature operators dominate, and the condition coincides parametrically with the positivity bounds that flat-space graviton amplitudes impose under standard assumptions on the ultraviolet completion. Only in scalar--tensor theories could the two-scale window probe beyond positivity, and then at most one family of dimension-ten operators. The axial sector of Einstein--dilaton--Gauss--Bonnet gravity and Einstein--Maxwell theory illustrate these results.
Related
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BibTeX
@misc{juliano2026quasinormalmode,
title = {{Quasinormal-mode stability bounds in gravitational EFT: resolvability, predictivity, and positivity}},
author = {Leonardo Juliano and Enrico Trincherini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28721},
eprint = {2610.28721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasinormal-mode stability bounds in gravitational EFT: resolvability, predictivity, and positivity
AU - Leonardo Juliano
AU - Enrico Trincherini
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28721
UR - https://arxiv.org/abs/2610.28721
AB - It has been proposed that consistency limits how slowly black holes can ring down in extensions of General Relativity: effective-field-theory (EFT) corrections may lengthen the decay time of a quasinormal mode by at most about one oscillation period, ℜ[ω_GR] δτ≲1. We argue that, under standard power counting, this condition yields no new, model-independent constraint on gravitational EFTs. First, its motivation does not extend straightforwardly to black holes: the inverse oscillation frequency is not a universal, detector-independent uncertainty in the damping time of a classical waveform. Our main argument, however, rests on eikonal power counting alone. The decay-time shift grows with the angular momentum ℓ of the mode, but so does the weight of higher-derivative operators. When curvature and derivatives are controlled by a single scale Λ, as in every known ultraviolet completion, the EFT around a black hole of radius r_s remains predictive up to ℓ∼(r_sΛ)^2, and the shift becomes of order one only there, where an infinite tower of operators contributes at the same order. A resolvable shift within the predictive regime requires either large numerical coefficients or a two-scale power counting, which has no known ultraviolet completion. In both cases the quartic-curvature operators dominate, and the condition coincides parametrically with the positivity bounds that flat-space graviton amplitudes impose under standard assumptions on the ultraviolet completion. Only in scalar--tensor theories could the two-scale window probe beyond positivity, and then at most one family of dimension-ten operators. The axial sector of Einstein--dilaton--Gauss--Bonnet gravity and Einstein--Maxwell theory illustrate these results.
ER -