Linear stability of Einstein-Gauss-Bonnet static spacetimes: Vector and scalar perturbations
Open accessAbstract
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form ${\ensuremath{\Sigma}}_{\ensuremath{\kappa}}^{n}\ifmmode\times\else\texttimes\fi{}{\mathbb{R}}^{+}$, ${\ensuremath{\Sigma}}_{\ensuremath{\kappa}}^{n}$ an $n\ensuremath{-}$manifold of constant curvature $\ensuremath{\kappa}$. Linear perturbations for this class of spacetimes can be generally classified into tensor, vector and scalar types. In a previous paper, tensor perturbations were analyzed. In this paper we study vector and scalar perturbations. We show that vector perturbations can be analyzed in general using an $S$-deformation approach and do not introduce instabilities. On the other hand, we show by analyzing an explicit example that, contrary to what happens in Einstein gravity, scalar perturbations may lead to instabilities in black holes with spherical horizons when the Gauss-Bonnet string corrections are taken into account.
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For a d = 5 small spherical black hole with Λ = 0, the scalar modes have V_eff < 0 near the horizon, giving the instability discovered in [20]; c_S < 0 implies the theory is not hyperbolic near the horizon.
“For the d = 5 example, the plot for the scalar modes reveals that < V 0 eff near the horizon.This gives rise to the instability discovered in [20].However, from our perspective this is much worse than an instability: < c 0 S implies that the theory is not hyperbolic near the horizon.”
From Causality and hyperbolicity of Lovelock theories (2014) · cites this paper as [20]
For static spherically or planar symmetric black hole solutions of Lovelock theories, there exist effective metrics G_S, G_V and G_T such that characteristic hypersurfaces are null hypersurfaces with respect to one of these metrics.
“From this one can infer that there exist 'effective metrics' G ab S , G ab V and G ab T such that characteristic hypersurfaces are null hypersurfaces with respect to one of these metrics.”
From Causality and hyperbolicity of Lovelock theories (2014) · cites this paper as [20]
The Introduction and Conclusions discuss tensor, vector, and scalar perturbations of Einstein–Gauss–Bonnet spacetimes as a stability problem. Searches for “effective metric,” “characteristic,” and “null hypersurface” found no passage stating that characteristic hypersurfaces are null with respect to sector-specific effective metrics. (LLM, conf=0.76)
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Causality and hyperbolicity of Lovelock theories
Reall, H. S., Tanahashi, N., & Way, B. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/20/205005 · Cited by 92 · see citing works
- Authors
- Gleiser, R. J., & Dotti, G.
- Affiliations
- Universidad Nacional de Córdoba (AR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2005-12-02
- Volume
- 72
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2035066338
- Cited by
- 135
- References
- 1
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 9 · 2023: 1 · 2022: 3 · 2021: 3 · 2020: 11 · 2019: 6 · 2018: 5 · 2017: 10 · 2016: 7 · 2015: 4 · 2014: 6 · 2013: 8 · 2012: 5
- FWCI
- 3.59
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Einstein-Gauss-Bonnet gravity, static spacetimes, linear stability, vector perturbations, scalar perturbations, black holes, higher-dimensional gravity, string corrections
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