Entropy current in conformal hydrodynamics

By R. Loganayagam. 2008

175 citations recorded by the source corpus.

In recent work [1, 2], the energy-momentum tensor for the = 4 SYM fluid was computed up to second derivative terms using holographic methods. The aim of this note is to propose an entropy current (accurate up to second derivative terms) consistent with this energy-momentum tensor and to explicate its relation with the existing theories of relativistic hydrodynamics. In order to achieve this, we first develop a Weyl-covariant formalism which simplifies the study of conformal hydrodynamics. This naturally leads us to a proposal for the entropy current of an arbitrary conformal fluid in any spacetime (with 3$>d>3). In particular, this proposal translates into a definite expression for the entropy flux in the case of = 4 SYM fluid. We conclude this note by comparing the formalism presented here with the conventional Israel-Stewart formalism.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4ebc96063129da929764fc7a9065b1d7ba728326

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, methodology): “f the structure of the conformal symmetry to present the answer compactly in a Weyl covariant form. We therefore will pause to review some details of this presentation following the beautiful work of [84]. The basic point is as follows: when we are discussing a conformal ﬁeld theory and the associat”
Relativistic viscous hydrodynamics, conformal invariance, and holography (2007, background): “Further detailed discussions on the issue of the local entropy current can be found in [50, 51].”
Adiabatic hydrodynamics: the eightfold way to dissipation (2015, methodology): “We further develop a Weyl covariant formulation of adiabatic hydrodynamics to deal with fluids arising from conformal field theories, extending [56], in Appendix D, where the reader can find some of the necessary details for the computations below.”
A Holographic View on Physics out of Equilibrium (2010, methodology): “Using a manifestly Weyl-covariant formalism [146], many of the expressions derived in [22] simplify.”
Hydrodynamics from charged black branes (2008, methodology): “32) where we have written the vectors in terms of the Weyl-covariant derivative introduced in [6].”
Relativistic viscous fluid dynamics and non-equilibrium entropy (2009, result): “rent must be of second order in gradients [20]. In the past, the form of the non-equilibrium entropy current has often be postulated [7]. More recently, a more fundamental approach has been advocated [21, 22] that calls for all structures in a gradient expansion to be allowed. I will follow this app”
Thermodynamics, gravitational anomalies and cones (2012, background): “Since gradients of Weyl covariant quantities generate non Weyl covariant expressions it is convenient to trade the gradient ∇μ with a Weyl covariant one ∇μ defined in [52].”
Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT (2008, unknown): “Contents”
Symmetry constraints on generalizations of Bjorken flow (2010, background): “(7)The Weyl covariant derivative introduced in [16] makes it substantially easier to check that σμν has ζ-weight −1.”
Fluid dynamics of R-charged black holes (2008, background): “See for example [29, 30, 31, 32, 33, 19, 15] for a more elaborate discussion on the construction of Weyl invariant quantities.”
Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions (2008, methodology): “6.1 AdS Kerr metrics as fluid duals 26 6.2 The Energy momentum tensor and the Entropy Current for the AdS Kerr Black Hole 28”
First-order relativistic hydrodynamics is stable (2019, unknown): “[9, 33].”
Weak Field Black Hole Formation in Asymptotically AdS Spacetimes (2009, background): “e the dynamical passage of a system from a (1)See [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] for a recent structural understanding of this connection.”
The incompressible non-relativistic Navier-Stokes equation from gravity (2008, background): “This may be simply achieved by taking the appropriate limit of the results of [4–13], and this limit is the topic of our note.”
The fluid/gravity correspondence: a new perspective on the membrane paradigm (2010, unknown): “This procedure of using the Weyl-covariant formalism [37] is so robust that we can equally easily write the form of a more general d-dimensional dissipative stress tensor for a conformal fluid living on a fixed background with metric γμν , to second order:”