Living Reviews in Relativity

"Relativistic Fluid Dynamics:
Physics for Many Different Scales"
Nils Andersson and Gregory L. Comer  

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1 Introduction
1.1 Setting the stage
1.2 A brief history of fluids
1.3 Notation and conventions
2 Physics in a Curved Spacetime
2.1 The metric and spacetime curvature
2.2 Parallel transport and the covariant derivative
2.3 The Lie derivative and spacetime symmetries
2.4 Spacetime curvature
3 The Stress-Energy-Momentum Tensor and the Einstein Equations
4 Why Are Fluids Useful Models?
5 A Primer on Thermodynamics and Equations of State
5.1 Fundamental, or Euler, relation
5.2 From microscopic models to the fluid equation of state
6 An Overview of the Perfect Fluid
6.1 Rates-of-change and Eulerian versus Lagrangian observers
6.2 The single, perfect fluid problem: “Off-the-shelf” consistency analysis
7 Setting the Context: The Point Particle
8 The “Pull-back” Formalism for a Single Fluid
9 The Two-Constituent, Single Fluid
10 The “Pull-Back” Formalism for Two Fluids
11 Speeds of Sound
11.1 Single fluid case
11.2 Two-constituent, single fluid case
11.3 Two fluid case
12 The Newtonian Limit and the Euler Equations
13 The CFS Instability
13.1 Lagrangian perturbation theory
13.2 Instabilities of rotating perfect fluid stars
13.3 The r-mode instability
13.4 The relativistic problem
14 Modelling Dissipation
14.1 The “standard” relativistic models
14.2 The Israel–Stewart approach
14.3 Carter’s canonical framework
14.4 Remaining issues
15 Heavy Ion Collisions
16 Superfluids and Broken Symmetries
16.1 Superfluids
16.2 Broken symmetries
17 Final Remarks
18 Acknowledgments
A The Volume Tensor
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