Stability of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">AdS</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>compactifications without supersymmetry

DeWolfe, Oliver; Freedman, Daniel Z.; Gubser, Steven S.; Horowitz, Gary T.; Mitra, Indrajit

doi:10.1103/physrevd.65.064033

Cited by 69 publications

(137 citation statements)

References 23 publications

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“…The first of these comprises generalisations to higher dimensions of the four-dimensional Schwarzschild black hole, in which the spatial 2-sphere at constant radius is generalised to a higher-dimensional Einstein space it arises from a consideration of the second variation of the Einstein-Hilbert action. We then review the black-hole stability [7] and AdS n × M d stability [12,13] criteria in sections 2.2 and 2.3, and in section 2.4 we review an argument given in [9,10] which shows how a lower bound on the Lichnerowicz spectrum can be obtained by considering the eigenvalues of the Weyl tensor.…”

Section: Stability and The Lichnerowicz Laplacianmentioning

confidence: 99%

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Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons

2003

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We study physical applications of the Bohm metrics, which are infinite sequences of inhomogeneous Einstein metrics on spheres and products of spheres of dimension 5 ≤ d ≤ 9.We prove that all the Bohm metrics on S 3 × S 2 and S 3 × S 3 have negative eigenvalue modes of the Lichnerowicz operator acting on transverse traceless symmetric tensors, and by numerical methods we establish that Bohm metrics on S 5 have negative eigenvalues too. General arguments suggest that all the Bohm metrics will have negative Lichnerowicz modes. These results imply that generalised higher-dimensional black-hole spacetimes, in which the Bohm metric replaces the usual round sphere metric, are classically unstable.We also show that the classical stability criterion for Freund-Rubin solutions, which are products of Einstein metrics with anti-de Sitter spacetimes, is the same in all dimensions as that for black-hole stability, and hence such solutions based on the Bohm metrics will also be unstable. We consider possible endpoints of the instabilities, and in particular we show that all Einstein-Sasaki manifolds give stable solutions. Next, we show how analytic continuation of Bohm metrics gives Lorentzian metrics that provide counterexamples to a strict form of the Cosmic Baldness conjecture, but they are nevertheless consistent with the intuition behind the cosmic No-Hair conjectures. We indicate how these Lorentzian metrics may be created "from nothing" in a no-boundary setting. We argue that Lorentzian Bohm metrics are unstable to decay to de Sitter spacetime. Finally, we argue that noncompact versions of the Bohm metrics have infinitely many negative Lichernowicz modes, and we conjecture a general relationship between Lichnerowicz eigenvalues and non-uniqueness of the Dirichlet problem for Einstein's equations.

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Section: Stability and The Lichnerowicz Laplacianmentioning

confidence: 99%

“…It was shown in [12,13] that the dangerous mode is a transverse tracefree mode on the manifold B multiplying a scalar on the AdS spacetimê…”

Section: Anti-de Sitter Product Spacetimesmentioning

confidence: 99%

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Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons

2003

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“…So a result on geometric stability of H n under Ricci flow would at least imply stability of H p × S q under a special class of metric perturbations and would be the first step towards a complete stability analysis of H p × S q . We also wish to mention that the classical stability of AdS p × S q in supergravity has been well-studied [31].…”

Section: Rg Flows In Closed String Theory Linear and Geometric Stmentioning

confidence: 99%

A proposal for studying off-shell stability of vacuum geometries in string theoryThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

Suneeta

2009

Can. J. Phys.

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We briefly review studies of off-shell stability of vacuum geometries in semiclassical gravity. We propose a study of off-shell stability of vacua in string theory by a distinct, though somewhat related approach -by studying their stability under suitable world-sheet sigma model renormalization group (RG) flows. Stability under RG flow is a mathematically well-posed and tractable problem in many cases, as we illustrate through examples. The advantage is that we can make definite predictions about late time behaviour and endpoints of off-shell processes in string theory. This is a contribution to the proceedings of Theory Canada 4, CRM Montreal.

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“…preserve some supersymmetry and hence are stable, making a geometric transition to these less symmetric spaces viable. Stable but non-supersymmetric vacuum solutions also exist and their stability can be analysed by looking at the eigenvalues of the Lichnerowicz operator acting on some tensor fields on the internal manifold (please see [11] for some recent work). Similar methods can be adopted to study the vacuum solutions that I considered in this paper.…”

Section: Transition and Reductionmentioning

confidence: 99%

Symmetry breaking of gauge theories via internal space dynamics

Biswas¹

2003

J. High Energy Phys.

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In this paper, I explain how gauge symmetry can be broken in a geometric way,à la Kaluza-Klein. In higher dimensional gravitational theories, one usually considers the extra dimensions to be "frozen" in time. However, the internal manifold is actually a dynamic entity. For example, its metric can change even if one expects its topological properties to be invariant. It is conceivable then, that at an earlier epoch the internal manifold made a geometric transition from say a maximally symmetric metric space to a less symmetric one. We know in a Kaluza-Klein reduction scheme, the massless gauge bosons are associated with the Killing vectors of the internal manifold. After the transition of the internal manifold, the gauge bosons associated with the broken Killing isometries will pick up a mass thereby breaking the gauge invariance partially. In this paper, I explore this idea, work out the mass of broken gauge bosons for some simple examples, and also point out how a mechanism similar to that of Higgs may be at work.

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Stability ofAdSp×Mqcompactifications without supersymmetry

Cited by 69 publications

References 23 publications

Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons

Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons

A proposal for studying off-shell stability of vacuum geometries in string theoryThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

Symmetry breaking of gauge theories via internal space dynamics

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