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Physical Review D 87 (2013) 061502
AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
Marco M. Caldarelli1, 2, 3, Joan Camps4, 5, B. Goutéraux6, 7, 8, 9, Kostas Skenderis3, 10

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.
1:  LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2:  CPHT - Centre de Physique Théorique [Palaiseau]
3:  School of Mathematics
4:  DAMTP/CMS - Department of Applied Mathematics and Theoretical Physics / Centre for Mathematical Sciences
5:  Dept. of Mathematical Sciences & CPT
6:  Nordita
7:  Crete Center for Theoretical Physics
8:  APC - UMR 7164 - AstroParticule et Cosmologie
9:  Physics Department
10:  Korteweg-de Vries Institute for Mathematics
Physics/General Relativity and Quantum Cosmology

Physics/High Energy Physics - Theory
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