Abstract
We describe the dynamics of two-dimensional relativistic and Carrollian fluids. These are mapped holographically to three-dimensional locally anti-de Sitter and locally Minkowski spacetimes, respectively. To this end, we use Eddington–Finkelstein coordinates, and grant general curved two-dimensional geometries as hosts for hydrodynamics. This requires to handle the conformal anomaly, and the expressions obtained for the reconstructed bulk metrics incorporate non-conformal-fluid data. We also analyze the freedom of choosing arbitrarily the hydrodynamic frame for the description of relativistic fluids, and propose an invariant entropy current compatible with classical and extended irreversible thermodynamics. This local freedom breaks down in the dual gravitational picture, and fluid/gravity correspondence turns out to be sensitive to dissipation processes: the fluid heat current is a necessary ingredient for reconstructing all Bañados asymptotically anti-de Sitter solutions. The same feature emerges for Carrollian fluids, which enjoy a residual frame invariance, and their Barnich–Troessaert locally Minkowski duals. These statements are proven by computing the algebra of surface conserved charges in the fluid-reconstructed bulk three-dimensional spacetimes.
Highlights
The first of the above three features raises another important question, regarding the role played by the boundary fluid congruence
We remind that the velocity field of a relativistic fluid can be chosen freely, altering neither the energy–momentum tensor nor the entropy current, but only transforming the various pieces that enter the decomposition of these quantities with respect to its longitudinal and transverse directions [12]
Analyzing the role of the velocity field in the fluid/gravity derivative expansion is not an easy task. This derivative expansion is organized in the form of a series, whose order is set by the derivatives of the velocity field, and which is designed to comply with Weyl covariance
Summary
The last term of (2.14) drops, whereas following the fluid equations (2.31) at zero external force (f = fμdxμ = 0), the forms √ε ± χ (u ± ∗u) are closed, and can be used to define a privileged light-cone coordinate system, adapted to the fluid configuration In this specific case, the on-shell Weyl scalar curvature reads. There is no generic and closed expression in terms of the dissipative tensors for this current, which is generally constructed order by order as a derivative expansion (see [29]) Whether this expansion can be hydrodynamic-frame invariant, and at the same time compatible with the underlying already quoted microscopic laws (unitarity and causality) as well as with the second law of thermodynamics is not known in full generality, this is in principle part of the rationale behind frame invariance. Τx′ x a 1 + k2 (β · B + (β + B) · b) 2 τ (1 − k2β2) (1 − k2B2)
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