- Title Pages
- I Lorentz Geometry
- II Special Relativity
- III General Relativity and Einstein's Equations
- IV Schwarzschild Spacetime and Black Holes
- V Cosmology
- VI Local Cauchy Problem
- VII Constraints
- VIII Other Hyperbolic-Elliptic Well-Posed Systems
- IX Relativistic Fluids
- X Relativistic Kinetic Theory
- XI Progressive Waves
- XII Global Hyperbolicity and Causality
- XIII Singularities
- XIV Stationary Spacetimes and Black Holes
- XV Global Existence Theorems: Asymptotically Euclidean Data
- XVI Global Existence Theorems: The Cosmological Case
- APPENDIX I Sobolev Spaces on Riemannian Manifolds
- APPENDIX II Second-Order Elliptic Systems on Riemannian Manifolds
- Appendix III Quasi-Diagonal, Quasi-Linear, Second-Order Hyperbolic Systems
- APPENDIX IV General Hyperbolic Systems
- APPENDIX V Cauchy–Kovalevski and Fuchs Theorems
- APPENDIX VI Conformal Methods
- APPENDIX VII Kaluza–Klein Theories
- Related Papers
- Causality of Classical Supergravity Yvonne Choquet-Bruhat I.M.T.A, Université Paris 6.
- Gravitation with Gauss Bonnet Terms Yvonne Choquet-Bruhat Abstract We study general properties of the partial differential equations for generalized gravity arising from the Lovelock Lagrangian.
- Interaction of Gravitational and Fluid Waves. Yvonne Choquet-Bruhat and Antonio Greco
- Course 6 Positive-Energy Theorems
- (p.259) IX Relativistic Fluids
- General Relativity and the Einstein Equations
- Oxford University Press
This chapter presents general properties of perfect fluids. When appropriate definitions are given, some of these properties generalize well-known properties of non-relativistic perfect fluids. However, the equivalence of mass and energy in Relativity introduces some fundamental differences. The limitation by the speed of light of the speed of any macroscopically transmitted signal also leads to new considerations. Topics covered include the case of dust, charged dust; perfect fluid, Euler equations; energy properties, particle number conservation, thermodynamics; wave fronts, propagation speeds, shocks; stationary motion, dynamic velocity for barotropic fluids, general perfect fluids, hyperbolic Leray system, first-order symmetric hyperbolic system, charged fluids, fluids with finite conductivity, magnetohydrodynamics, Yang–Mills fluids, and dissipative fluids.
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