Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
From Navier-Stokes To Einstein
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For $p=2$, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence.
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Establishes a holographic link between bulk gravitational radiation and dissipative corrections plus entropy production in boundary fluids, then constructs Carrollian analogues and celestial observables in the flat limit.
Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.
citing papers explorer
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Fluid dynamics as intersection problem
Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
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Radiation in Fluid/Gravity and the Flat Limit
Establishes a holographic link between bulk gravitational radiation and dissipative corrections plus entropy production in boundary fluids, then constructs Carrollian analogues and celestial observables in the flat limit.
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Holographic pressure and volume for black holes
Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.