Gravitational instability of Einstein–Gauss–Bonnet black holes under tensor mode perturbations
Open accessAbstract
We analyse the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss–Bonnet term in dimension D > 4. We show that the evolution equations for this type of perturbation can be cast in a Regge–Wheeler–Zerilli form, and obtain the exact potential for the corresponding Schrödinger-like stability equation. As an immediate application we prove that for D ≠ 6 and α > 0, the sign choice for the Gauss–Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case D = 6, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for α < 0.
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For bad modes, V_l is negative for r <= r_bad and admits negative energy bound states.
“But for the bad modes, V r ( ) l is negative for ⩽ r r bad , and admits negative energy bound states [18].”
From Causality and hyperbolicity of Lovelock theories (2014) · cites this paper as [18]
Section 3 gives a negative-potential-integral criterion for negative-energy bound states and shows it holds for sufficiently small mass and large angular eigenvalue in the exceptional n = 4 case. The copy does not define r_bad or establish that the potential is negative throughout r ≤ r_bad. No page number is available for these passages in the indexed copy. (LLM, conf=0.83)
Experimental — accuracy not yet measuredFor a d = 6 small spherical black hole with Λ = 0, the tensors have V_eff < 0 near the horizon, giving the instability of [18,19]; this is a failure of hyperbolicity.
“Similarly, for the d = 6 example the tensors have < V 0 eff near the horizon, which gives the instability of [18,19].But again, this is much worse than an instability, it is a failure of hyperbolicity of the theory.”
From Causality and hyperbolicity of Lovelock theories (2014) · cites this paper as [18]
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 [18]
Section 2 (pp. L2–L3) studies tensor perturbations of spherically symmetric Einstein–Gauss–Bonnet solutions, and Section 4 (p. L6) summarizes a stability analysis. Our copy does not address effective metrics for scalar, vector, and tensor modes or say that characteristic hypersurfaces are null with respect to them (searched: effective metrics, characteristic hypersurfaces, and propagation cones). (LLM, conf=0.76)
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String-Generated Gravity Models
Boulware, D. G., & Deser, S. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.2656 · Cited by 1,583 · see citing works
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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
- Dotti, G., & Gleiser, R. J.
- Affiliations
- Universidad Nacional de Córdoba (AR)
- ORCID
- Dotti, Gustavo
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2004-12-10
- Volume
- 22
- Issue
- 1
- Pages
- L1-L6
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1984446792
- Cited by
- 116
- References
- 1
- Citations by year
- 2026: 16 · 2025: 9 · 2024: 7 · 2023: 2 · 2021: 2 · 2020: 3 · 2019: 6 · 2018: 3 · 2017: 4 · 2016: 4 · 2015: 2 · 2014: 4 · 2013: 5 · 2012: 3
- FWCI
- 2.97
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0204937)
- Agencia Córdoba Ciencia
- Consejo Nacional de Investigaciones Científicas y Técnicas
- Universidad de Córdoba
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Pulsars and Gravitational Waves Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- gravitational instability, Einstein-Gauss-Bonnet gravity, black holes, higher-dimensional black holes, six-dimensional black holes, asymptotically flat black holes, static spherically symmetric solutions
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