AdS/Ricci-flat correspondence and the Gregory-Laflamme instability

Abstract : We show that for every asymptotically AdS solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). This correspondence should allow us to develop a holographic dictionary for Ricci-flat spacetimes. In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress energy tensor of AdS to the stress energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. Applying it to the known solutions describing the hydrodynamic regime in AdS/CFT we compute the dispersion relation of the Gregory-Laflamme unstable modes through cubic order in the wavenumber finding remarkable agreement with numerical data.
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Journal articles
Physical Review D, American Physical Society, 2013, 87, pp.061502. <10.1103/PhysRevD.87.061502>


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Submitted on : Thursday, November 15, 2012 - 3:47:03 PM
Last modification on : Tuesday, October 28, 2014 - 6:16:49 PM

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Marco M. Caldarelli, Joan Camps, B. Goutéraux, Kostas Skenderis. AdS/Ricci-flat correspondence and the Gregory-Laflamme instability. Physical Review D, American Physical Society, 2013, 87, pp.061502. <10.1103/PhysRevD.87.061502>. <hal-00752386>

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