Living Reviews in Relativity

"The Einstein–Vlasov System/Kinetic Theory"
Håkan Andréasson  

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1 Introduction to Kinetic Theory
1.1 The relativistic Boltzmann equation
1.2 The Vlasov–Maxwell and Vlasov–Poisson systems
1.3 The Nordström–Vlasov system
2 The Einstein–Vlasov System
3 The Asymptotically-Flat Cauchy Problem: Spherically-Symmetric Solutions
3.1 Set up and choice of coordinates
3.2 Local existence and the continuation criterion
3.3 Global existence for small initial data
3.4 Global existence for special classes of large initial data
3.5 On global existence for general initial data
3.6 Self-similar solutions
3.7 Formation of black holes and trapped surfaces
3.8 Numerical studies on critical collapse
3.9 The charged case
4 The Cosmological Cauchy Problem
4.1 Spatially-homogeneous spacetimes
4.2 Inhomogeneous models with symmetry
4.3 Cosmological models with a scalar field
4.4 Stability of some cosmological models
5 Stationary Asymptotically-Flat Solutions
5.1 Existence of spherically-symmetric static solutions
5.2 The structure of spherically-symmetric steady states
5.3 Buchdahl-type inequalities
5.4 Stability
5.5 Existence of axisymmetric static solutions
6 Acknowledgements
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