Abstract
We consider Einstein gravity in AdS in the presence of a deformed conformal boundary metric, in the limit of large spacetime dimension. At leading order we find a new set of effective near-horizon equations. These can be understood as covariant generalisations of the undeformed equations with new source terms due to the curvature. We show that these equations are given by the conservation of the exact second-order Landau-frame hydrodynamic stress tensor. No derivative expansions are invoked in this identification. We use the new equations to study CFTs with 2d lattice deformations, computing their quasi-normal mode spectra and thermal conductivities, both numerically and analytically to quartic order in small lattice amplitude. Many of our results also apply to asymptotically flat spacetimes.
Highlights
That depend on the directions on the horizon [5,6,7,8,9]
We show that these equations are given by the conservation of the exact second-order Landau-frame hydrodynamic stress tensor
A key result of our work is a new set of effective near-horizon equations at leading order in 1/d which includes these metric deformations
Summary
With these definitions, the constitutive relations of conformal relativistic hydrodynamics in Landau-frame, truncated to second order in derivatives can be written [36]. Let us interpret our results in terms of the usual transport coefficients given in equation (3.9) To achieve this we start by making two observations: the first one is that, given (3.25) and (3.26), all transport coefficients scale like ∼ n−2 and the second one is that they all have the same units as c1. These two points lead us to conclude that λiT , κT , (ητπ)T = O(n)0 . Gregory-Laflamme instabilities, as we will see more explicitly
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