A Gravitational instability in higher dimensions
By G. W. Gibbons, S. Hartnoll. 2002
168 citations recorded by the source corpus.
We explore a classical instability of spacetimes of dimension $Dg4.$ First, we consider static solutions: generalized black holes and brane world metrics. The dangerous mode is a tensor mode on an Einstein base manifold of dimension $D\ensuremath{-}2.$ A criterion for instability is found for the generalized Schwarzschild, AdS-Schwarzschild and topological black hole spacetimes in terms of the Lichnerowicz spectrum on the base manifold. Secondly, we consider perturbations in time-dependent solutions: Generalized dS and AdS. Thirdly we show that, subject to the usual limitations of a linear analysis, any Ricci flat spacetime may be stabilized by embedding into a higher dimensional spacetime with cosmological constant. We apply our results to pure AdS black strings. Finally, we study the stability of higher dimensional ``bubbles of nothing.''
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/3f1e79aa18cea254a1963a579f8ff517f695abf6
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Citations in the corpus
- GRAVITATIONAL PERTURBATIONS OF HIGHER DIMENSIONAL ROTATING BLACK HOLES (2006, unknown): “If we set a = 0 then we have a Schwarzschild(-AdS) black hole and our tensor perturbations should form a subset of the tensor perturbations considered in [4, 5, 6].”
- Topology change in general relativity, and the black-hole black-string transition (2002, background): “17) ([31], a closely related formula appeared yesterday in [32] eq.”
- Asymptotic black hole quasinormal frequencies (2003, background): “the potential is a particular family of tensor metric perturbations studied in [23], which exist only in d > 4; for these the leading singularity corresponds again to j = 0.”
- Black Holes in Higher Dimensions (2008, methodology): “For tensor modes, the potential in the Schrödinger equation is manifestly positive, hence ω(2) > 0 and there is no instability [105].”
- Gravity Dual of Spatially Modulated Phase (2009, background): “ is specied by 2(1) < 3, where ˚ 2(u) oscillates innitely many times as they approach the horizon as can be seen from (4.21). On general ground, we expect an instability to occur in this range [34]. Interestingly, the instability condition 2(1) < 3 of the near-horizon geometry is not necessa”
- Linear stability of Perelman's $ν$-entropy on symmetric spaces of compact type (2013, background): “the Freund-Rubin compactification, the stability condition of an Einstein manifold Mn with Einstein constant λ > 0 is given by µL ≥ − λ n−1 4− 1 4 (n−5)2 . From the estimates of µ fns and µL in [GH], [GHP], [GM], [PP1] and [PP2], the following examples are linearly unstable: (1) The three infinit”
- Constant mean curvature surfaces in warped product manifolds (2011, unknown): “nt scalar curvature n(n−1)κ. Proof. We consider the product M× R equipped with the Lorentzian metric g= −f2 dt⊗dt+g = −(1 −mr2−n −κr2)dt⊗dt+ 1 1−mr2−n −κr2 dr⊗dr+r2 g Sn−1. It is well known (see e.g. [8]) that the Lorentzian manifold (M×R,g) is a solution to the Einstein equations in dimensionn+1 wi”
- Landscape of superconducting membranes (2009, unknown): “many times before reaching the horizon [31].”
- Static response and Love numbers of Schwarzschild black holes (2020, background): “37) The equation of motion following from this action was derived in [69, 90].”
- An instability of higher-dimensional rotating black holes (2010, background): “In higher dimensions, the stability of the Schwarzschild solution against linearized gravitational perturbations has been established [11, 22, 20].”