REVIEW
The Gregory-Laflamme Instability of five-dimensional Black Strings in Einstein-Gauss-Bonnet Gravity
High Energy Physics - Theory · Submitted 9 Oct 2026 · 76 references
Pith's verdict: A clean, careful paper that shows when and how the EGB evolution breaks down for black strings, with an explicit effective-metric diagnostic. The central claim is well-supported, and the limitations are open and acknowledged.
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Referee report
The paper
The paper claims
Effective metric degeneracy rules out a class of black string solutions in Einstein-Gauss-Bonnet gravity
The reading
What carries the argument
The key is the effective metric $g^{ab}_{\rm eff}$ derived from the principal symbol of the symmetry-reduced Einstein-Gauss-Bonnet equations under $SO(3)$ symmetry. This metric differs from the spacetime metric by curvature terms proportional to $\lambda_{\rm GB}$. When it ceases to be Lorentzian—specifically when its spatially reduced eigenvalues become negative—the characteristic speeds are imaginary and the initial value problem becomes ill-posed. The paper derives a threshold $\lambda_{\rm GB}/r_H^2 > (\sqrt{2}-1)/4 \approx 0.104$ for uniform black strings, beyond which the effective metric degenerates on and near the horizon.
Extended reading notes
Core claim
The central discovery is that the condition for well-posed Cauchy evolution in Einstein-Gauss-Bonnet gravity—Lorentzian signature of an effective metric derived from the principal symbol—fails on a non-empty set of regular uniform black string solutions for any positive Gauss-Bonnet coupling. This set includes the uniform black string of minimal thickness that would otherwise be a plausible endpoint of the Gregory-Laflamme instability. Consequently, this endpoint cannot be reached by time evolution from generic initial data; the solutions of the linearized equations around these backgrounds are formal and do not approximate non-linear evolutions. The non-linear simulations corroborate this: they terminate through a Tricomi-type loss of hyperbolicity for positive coupling and a Keldysh-type for negative coupling, both inside the apparent horizon.
Load-bearing premise
The analysis assumes SO(3) symmetry in the asymptotically flat directions, which reduces the dynamics to a single physical degree of freedom; the derived bound on hyperbolicity may only be an upper bound because perturbations breaking this symmetry could lose hyperbolicity at smaller couplings.
Editorial extensions
If this is right
- Any uniform black string with $\lambda_{\rm GB}/r_H^2 > (\sqrt{2}-1)/4$ is dynamically inaccessible; thus the limiting string of minimal thickness $r_H = \sqrt{8\lambda_{\rm GB}}$ is not an attainable endpoint of the Gregory-Laflamme instability.
- Linear perturbation analyses on such backgrounds yield formal solutions that do not correspond to nearby non-linear evolutions; growth rates computed for couplings above the threshold are not physically meaningful.
- The non-linear Gregory-Laflamme instability in Einstein-Gauss-Bonnet gravity always terminates through a loss of hyperbolicity before the string reaches the thinness of the limiting static solution.
- For $\lambda_{\rm GB} < 0$, the effective metric remains Lorentzian on and outside the horizon, so the evolution may in principle continue closer to the singular limit, but practical simulations break down due to stiffness.
Reading between the lines
- The bound $\lambda_{\rm GB}/r_H^2 > (\sqrt{2}-1)/4$ is derived within the $SO(3)$-symmetric sector; perturbations breaking this symmetry may cause loss of hyperbolicity at smaller couplings, as the paper acknowledges. Therefore the actual range of well-posed evolution for generic black strings may be even narrower.
- This analysis provides a template for diagnosing the dynamical relevance of stationary solutions in effective field theories of gravity: one can test whether the effective metric of the symmetry-reduced system remains Lorentzian on and outside the horizon.
- The results suggest that if string theory or a UV completion resolves the Gregory-Laflamme endpoint, it must do so before the effective metric degenerates, i.e., at curvatures well below the string scale for positive Gauss-Bonnet coupling.
Original abstract
We complement and extend our recent study of the non-linear evolution of the Gregory-Laflamme instability of black strings in Einstein-Gauss-Bonnet gravity in five spacetime dimensions. First, we study time-dependent perturbations of uniform black strings in Einstein-Gauss-Bonnet theory and determine the growth rates as a function of the coupling. We find that for positive Gauss-Bonnet couplings, the black strings are more unstable than in general relativity in the sense that the growth rates are larger and shorter wavelengths are unstable. In the second part of the paper we show that the hyperbolicity of the equation of motion of Einstein-Gauss-Bonnet theory is determined by an effective metric when the dynamics is restricted to spherical symmetry in the asymptotically flat directions. When the effective field theory becomes strongly coupled, as it happens near the endpoint of the Gregory-Laflamme instability of the black string, this effective metric becomes degenerate and the Cauchy evolution breaks down. Applying this criterion to uniform black strings, we find that for any positive Gauss-Bonnet coupling there is an open set of regular solutions (including the one of minimal thickness) on which the effective metric degenerates in a neighbourhood of the horizon. Therefore, we argue that these solutions cannot be attained from weakly coupled initial data by Cauchy evolution and the solutions of the linearized equations around them cannot be interpreted as approximations to nearby non-linear evolutions. We provide further evidence for this picture with non-linear simulations of the Gregory-Laflamme instability. The non-linear simulations terminate through a loss of hyperbolicity of the Tricomi or Keldysh type, depending on the sign of the Gauss-Bonnet coupling.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We complement and extend our recent study of the non-linear evolution of the Gregory-Laflamme instability of black strings in Einstein-Gauss-Bonnet gravity in five spacetime dimensions. First, we study time-dependent perturbations of uniform black strings in Einstein-Gauss-Bonnet theory and determine the growth rates as a function of the coupling. We find that for positive Gauss-Bonnet couplings, the black strings are more unstable than in general relativity in the sense that the growth rates are larger and shorter wavelengths are unstable. In the second part of the paper we show that the hyperbolicity of the equation of motion of Einstein-Gauss-Bonnet theory is determined by an effective metric when the dynamics is restricted to spherical symmetry in the asymptotically flat directions. When the effective field theory becomes strongly coupled, as it happens near the endpoint of the Gregory-Laflamme instability of the black string, this effective metric becomes degenerate and the Cauchy evolution breaks down. Applying this criterion to uniform black strings, we find that for any positive Gauss-Bonnet coupling there is an open set of regular solutions (including the one of minimal thickness) on which the effective metric degenerates in a neighbourhood of the horizon. Therefore, we argue that these solutions cannot be attained from weakly coupled initial data by Cauchy evolution and the solutions of the linearized equations around them cannot be interpreted as approximations to nearby non-linear evolutions. We provide further evidence for this picture with non-linear simulations of the Gregory-Laflamme instability. The non-linear simulations terminate through a loss of hyperbolicity of the Tricomi or Keldysh type, depending on the sign of the Gauss-Bonnet coupling.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We complement and extend our recent study of the non-linear evolution of the Gregory-Laflamme instability of black strings in Einstein-Gauss-Bonnet gravity in five spacetime dimensions. | contribution 0.59 | 0.76 | 0.04 | asserted 0.82 |
| s1 | First, we study time-dependent perturbations of uniform black strings in Einstein-Gauss-Bonnet theory and determine the growth rates as a function of the coupling. | contribution 0.91 | 0.95 | 0.03 | asserted 0.93 |
| s2 | We find that for positive Gauss-Bonnet couplings, the black strings are more unstable than in general relativity in the sense that the growth rates are larger and shorter wavelengths are unstable. | result 0.99 | 0.96 | 0.12 | asserted 1.00 |
| s3 | In the second part of the paper we show that the hyperbolicity of the equation of motion of Einstein-Gauss-Bonnet theory is determined by an effective metric when the dynamics is restricted to spherical symmetry in the asymptotically flat directions. | contribution 0.79 | 0.89 | 0.07 | asserted 1.00 |
| s4 | When the effective field theory becomes strongly coupled, as it happens near the endpoint of the Gregory-Laflamme instability of the black string, this effective metric becomes degenerate and the Cauchy evolution breaks down. | result 0.78 | 0.70 | 0.15 | asserted 1.00 |
| s5 | Applying this criterion to uniform black strings, we find that for any positive Gauss-Bonnet coupling there is an open set of regular solutions (including the one of minimal thickness) on which the effective metric degenerates in a neighbourhood of the horizon. | result 1.00 | 0.95 | 0.20 | asserted 1.00 |
| s6 | Therefore, we argue that these solutions cannot be attained from weakly coupled initial data by Cauchy evolution and the solutions of the linearized equations around them cannot be interpreted as approximations to nearby non-linear evolutions. | interpretation 1.00 | 0.79 | 0.41 | asserted 0.47 |
| s7 | We provide further evidence for this picture with non-linear simulations of the Gregory-Laflamme instability. | contribution 0.49 | 0.92 | 0.05 | asserted 0.95 |
| s8 | The non-linear simulations terminate through a loss of hyperbolicity of the Tricomi or Keldysh type, depending on the sign of the Gauss-Bonnet coupling. | result 1.00 | 0.93 | 0.13 | asserted 1.00 |
What was examined, and what was not
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Figures
Showing 4 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.13612 by the authors.
References
Discussion
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