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

2012

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

Caldarelli, Marco M., Camps, Joan, Goutéraux, Blaise et al.

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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).

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 derive the hydrodynamic stress-tensor of asymptotically flat black branes to second order, which is constrained by the parent conformal symmetry.
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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