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Nonperturbative suppression of beyond-General-Relativity effects in quadratic gravity
General Relativity and Quantum Cosmology · Submitted 2 Apr 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here, by studying the gravitational-wave emission from point particles plunging into a Schwarzschild black hole in quadratic gravity, we show that observable deviations from GR are exponentially suppressed in the GR limit.
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The abstract, sentence by sentence
Quadratic gravity is a well-motivated extension of general relativity~(GR) wherein the Einstein-Hilbert action is augmented by quadratic curvature terms. This theory is equivalent to GR in an effective-field-theory framework, while the two theories are different at the non-perturbative level. As we have recently shown, black holes in quadratic gravity have a rich linear response, including extra scalar, vector, and tensor quasinormal modes that can be excited in physical processes, even when the stationary solution is the same as in GR. Here, by studying the gravitational-wave emission from point particles plunging into a Schwarzschild black hole in quadratic gravity, we show that observable deviations from GR are exponentially suppressed in the GR limit. This provides a nonperturbative realization of the equivalence between quadratic gravity and GR predicted in the effective-field-theory framework.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Quadratic gravity is a well-motivated extension of general relativity~(GR) wherein the Einstein-Hilbert action is augmented by quadratic curvature terms. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | This theory is equivalent to GR in an effective-field-theory framework, while the two theories are different at the non-perturbative level. | background 0.98 | 0.11 | 0.05 | asserted 1.00 |
| s2 | As we have recently shown, black holes in quadratic gravity have a rich linear response, including extra scalar, vector, and tensor quasinormal modes that can be excited in physical processes, even when the stationary solution is the same as in GR. | background 0.80 | 0.80 | 0.04 | asserted 0.93 |
| s3 | Here, by studying the gravitational-wave emission from point particles plunging into a Schwarzschild black hole in quadratic gravity, we show that observable deviations from GR are exponentially suppressed in the GR limit. | result 0.92 | 0.96 | 0.94 | asserted 1.00 |
| s4 | This provides a nonperturbative realization of the equivalence between quadratic gravity and GR predicted in the effective-field-theory framework. | interpretation 1.00 | 0.64 | 0.17 | asserted 1.00 |
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The paper
Original abstract
Quadratic gravity is a well-motivated extension of general relativity~(GR) wherein the Einstein-Hilbert action is augmented by quadratic curvature terms. This theory is equivalent to GR in an effective-field-theory framework, while the two theories are different at the non-perturbative level. As we have recently shown, black holes in quadratic gravity have a rich linear response, including extra scalar, vector, and tensor quasinormal modes that can be excited in physical processes, even when the stationary solution is the same as in GR. Here, by studying the gravitational-wave emission from point particles plunging into a Schwarzschild black hole in quadratic gravity, we show that observable deviations from GR are exponentially suppressed in the GR limit. This provides a nonperturbative realization of the equivalence between quadratic gravity and GR predicted in the effective-field-theory framework.
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References
How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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In this context, QNMs in higher-curvature or EFT-modified gravity theories have also been studied extensively, see, e.g., Refs. [ref] .
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing · Introduction · 0.87
What it cites · 40 sentences without a confident label
Uses the method or tool of 11 papers
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We use the Noether current approach, in which the stress-energy tensor is derived as the conserved current associated to diffeomorphism invariance [ref] .
The Gravitational Wave Stress-Energy (pseudo)-Tensor in Modified Gravity · GW stress-energy tensor · 1.00
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We expand the action to quadratic order in the perturbations [equation] where $S^(0)$ corresponds to the background action, $S^(1)$ vanishes upon short-wavelength averaging [ref] , and $S^(2)$ encodes the effective GW dynamics.
Effective Gravitational Wave Stress-energy Tensor in Alternative Theories of Gravity · GW stress-energy tensor · 0.82
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To solve the system of inhomogeneous differential equations we will employ the Green's matrix approach [ref] which we summarize in Appendix [ref].
Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator · Solutions with a source · 1.00
Uses data or values from 1 paper
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Finally, hairy black holes exist only below a critical mass, $M_c ≃0.438/μ$ [ref] .
Black Holes in Higher-Derivative Gravity · Black hole solutions · 0.89
Compares with 3 papers
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As shown in the bottom panel of Fig. [ref], the total monopole energy flux has a maximum around $μM≈0.08$ and decays linearly to zero in the strong-coupling regime ($μM→0$, $α→∞$, see inset), in agreement with the analysis of [ref] in massive gravity.
Gravitational waves in massive gravity theories: waveforms, fluxes and constraints from extreme-mass-ratio mergers · Monopolar radiation · 0.98
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The curves confirm the presence of an instability for $Mμ<0.43$, consistently with the results of [ref] .
Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass · Radial instability of monopolar perturbations · 0.86
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The curves confirm the presence of an instability for $Mμ<0.43$, consistently with the results of [ref] .
Time Evolution of Black Hole Perturbations in Quadratic Gravity · Radial instability of monopolar perturbations · 0.86
Cites as support 1 paper
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We remark that, as we argue in [ref] , it is unlikely that current astrophysical observations of black holes probe the strong-field regime of quadratic gravity (see also the discussion in Sec. [ref]).
Gravitational quasinormal modes of black holes in quadratic gravity · Introduction · 0.99
Cites as background 14 papers
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As previously mentioned, these equations are equivalent to those of massive gravity [ref] , which have been studied in [ref] in the context of black hole perturbations.
Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass · Master equations · 0.80
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Recent work has explored black hole solutions [ref] , stability analyses [ref] , perturbative [ref] and post-Newtonian [ref] studies, and numerical simulations [ref] , aiming to understand the full nonlinear dynamics of the theory and its potential observational signatures.
Black Holes in Higher-Derivative Gravity · Introduction · 0.88
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Recent work has explored black hole solutions [ref] , stability analyses [ref] , perturbative [ref] and post-Newtonian [ref] studies, and numerical simulations [ref] , aiming to understand the full nonlinear dynamics of the theory and its potential observational signatures.
Spherically Symmetric Solutions in Higher-Derivative Gravity · Introduction · 0.88
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