
Abstract 
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
StressEnergyMomentum 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 
Ratesofchange
and Eulerian versus Lagrangian observers 

6.2 
The single, perfect fluid
problem: “Offtheshelf” consistency analysis 
7 
Setting the Context:
The Point Particle 
8 
The “Pullback” Formalism for a Single Fluid 
9 
The
TwoConstituent, Single Fluid 
10 
The “PullBack” Formalism for Two
Fluids 
11 
Speeds of Sound 

11.1 
Single fluid case 

11.2 
Twoconstituent,
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 rmode
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 

References 

Footnotes 

Figures 