Abstract
The fluid-gravity correspondence documents a precise mathematical map between a class of dynamical spacetime solutions of the Einstein field equations of gravity and the dynamics of its corresponding dual fluid flows governed by the Navier-Stokes (NS) equations of hydrodynamics. This striking connection has been explored in several dynamics-based approaches and has surfaced in various forms over the past four decades. In a recent construction, it has been shown that the manifold properties of geometric duals are in fact intimately connected to the dynamics of incompressible fluids, thus bypassing the conventional on-shell standpoints. Following such a prescription, we construct the geometrical description that effectively captures the dynamics of an incompressible NS fluid with respect to a uniformly rotating frame. We propose the gravitational dual(s) described by bulk metric(s) in () dimensions such that the equations of parallel transport of an appropriately defined bulk velocity vector field when projected onto an induced timelike hypersurface require that the incompressible NS equation of a fluid relative to a uniformly rotating frame be satisfied at the relevant perturbative order in () dimensions. We argue that free fluid flows on manifold(s) described by the proposed metric(s) can be effectively considered as an equivalent theory of nonrelativistic viscous fluid dynamics with respect to a uniform rotating frame. We also present suggestive insights as to how spacetime rotation parameters encode information pertaining to the inertial effects in the corresponding fluid dual.
- Received 2 May 2020
- Accepted 10 August 2020
DOI:https://doi.org/10.1103/PhysRevD.102.064003
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Published by the American Physical Society