| Selected Solutions of Einstein's Field Equations: Their Role in General Relativity and Astrophysics | p. 1 |
| Introduction and a Few Excursions | p. 1 |
| A Word on the Role of Explicit Solutions in Other Parts of Physics and Astrophysics | p. 3 |
| Einstein's Field Equations | p. 5 |
| "Just So" Notes on the Simplest Solutions: The Minkowski, de Sitter, and Anti-de Sitter Spacetimes | p. 8 |
| On the Interpretation and Characterization of Metrics | p. 11 |
| The Choice of Solutions | p. 15 |
| The Outline | p. 17 |
| The Schwarzschild Solution | p. 19 |
| Spherically Symmetric Spacetimes | p. 19 |
| The Schwarzschild Metric and Its Role in the Solar System | p. 20 |
| Schwarzschild Metric Outside a Collapsing Star | p. 21 |
| The Schwarzschild-Kruskal Spacetime | p. 25 |
| The Schwarzschild Metric as a Case Against Lorentz-Covariant Approaches | p. 28 |
| The Schwarzschild Metric and Astrophysics | p. 29 |
| The Reissner-Nordström Solution | p. 31 |
| Reissner-Nordström Black Holes and the Question of Cosmic Censorship | p. 32 |
| On Extreme Black Holes, d-Dimensional Black Holes, String Theory and "All That" | p. 39 |
| The Kerr Metric | p. 42 |
| Basic Features | p. 42 |
| The Physics and Astrophysics Around Rotating Black Holes | p. 47 |
| Astrophysical Evidence for a Kerr Metric | p. 50 |
| Black Hole Uniqueness and Multi-black Hole Solutions | p. 52 |
| On Stationary Axisymmetric Fields and Relativistic Disks | p. 55 |
| Static Weyl Metrics | p. 55 |
| Relativistic Disks as Sources of the Kerr Metric and Other Stationary Spacetimes | p. 57 |
| Uniformly Rotating Disks | p. 59 |
| Taub-NUT Space | p. 62 |
| A New Way to the NUT Metric | p. 62 |
| Taub-NUT Pathologies and Applications | p. 64 |
| Plane Waves and Their Collisions | p. 66 |
| Plane-Fronted Waves | p. 66 |
| Plane-Fronted Waves: New Developments and Applications | p. 71 |
| Colliding Plane Waves | p. 72 |
| Cylindrical Waves | p. 77 |
| Cylindrical Waves and the Asymptotic Structure of 3-Dimensional General Relativity | p. 78 |
| Cylindrical Waves and Quantum Gravity | p. 82 |
| Cylindrical Waves: a Miscellany | p. 85 |
| On the Robinson-Trautman Solutions | p. 86 |
| The Boost-Rotation Symmetric Radiative Spacetimes | p. 88 |
| The Cosmological Models | p. 93 |
| Spatially Homogeneous Cosmologies | p. 95 |
| Inhomogeneous Cosmologies | p. 102 |
| Concluding Remarks | p. 105 |
| References | p. 108 |
| The Cauchy Problem for the Einstein Equations | p. 127 |
| Introduction | p. 127 |
| Basic Observations and Concepts | p. 131 |
| The Principal Symbol | p. 132 |
| The Constraints | p. 135 |
| The Bianchi Identities | p. 137 |
| The Evolution Equations | p. 137 |
| Assumptions and Consequences | p. 146 |
| PDE Techniques | p. 147 |
| Symmetric Hyperbolic Systems | p. 147 |
| Symmetric Hyperbolic Systems on Manifolds | p. 157 |
| Other Notions of Hyperbolicity | p. 159 |
| Reductions | p. 164 |
| Hyperbolic Systems from the ADM Equations | p. 167 |
| The Einstein-Euler System | p. 173 |
| The Initial Boundary Value Problem | p. 185 |
| The Einstein-Dirac System | p. 193 |
| Remarks on the Structure of the Characteristic Set | p. 200 |
| Local Evolution | p. 201 |
| Local Existence Theorems for the Einstein Equations | p. 201 |
| Uniqueness | p. 204 |
| Cauchy Stability | p. 206 |
| Matter Models | p. 207 |
| An Example of an Ill-Posed Initial Value Problem | p. 214 |
| Symmetries | p. 216 |
| Outlook | p. 217 |
| References | p. 219 |
| Post-Newtonian Gravitational Radiation | p. 225 |
| Introduction | p. 225 |
| On Approximation Methods in General Relativity | p. 225 |
| Field Equations and the No-Incoming-Radiation Condition | p. 228 |
| Method and General Physical Picture | p. 231 |
| Multipole Decomposition | p. 233 |
| The Matching Equation | p. 233 |
| The Field in Terms of Multipole Moments | p. 236 |
| Equivalence with the Will-Wiseman Multipole Expansion | p. 238 |
| Source Multipole Moments | p. 240 |
| Multipole Expansion in Symmetric Trace-Free Form | p. 240 |
| Linearized Approximation to the Exterior Field | p. 241 |
| Derivation of the Source Multipole Moments | p. 242 |
| Post-Minkowskian Approximation | p. 244 |
| Multipolar Post-Minkowskian Iteration of the Exterior Field | p. 244 |
| The "Canonical" Multipole Moments | p. 246 |
| Retarded Integral of a Multipolar Extended Source | p. 247 |
| Radiative Multipole Moments | p. 248 |
| Definition and General Structure | p. 249 |
| The Radiative Quadrupole Moment to 3PN Order | p. 250 |
| Tail Contributions in the Total Energy Flux | p. 251 |
| Post-Newtonian Approximation | p. 253 |
| The Inner Metric to 2.5PN Order | p. 254 |
| The Mass-Type Source Moment to 2.5PN Order | p. 256 |
| Point-Particles | p. 258 |
| Hadamard Partie Finie Regularization | p. 259 |
| Multipole Moments of Point-Mass Binaries | p. 261 |
| Equations of Motion of Compact Binaries | p. 263 |
| Gravitational Waveforms of Inspiralling Compact Binaries | p. 265 |
| Conclusion | p. 267 |
| Duality and Hidden Symmetries in Gravitational Theories | p. 273 |
| Introduction | p. 273 |
| Electromagnetic Duality | p. 277 |
| Duality in Kaluza-Klein Theories | p. 279 |
| Dimensional Reduction from D to d Dimensions | p. 280 |
| Reduction to d = 4 Dimensions | p. 282 |
| Reduction to d =3 Dimensions | p. 285 |
| Reduction to d = 2 Dimensions | p. 290 |
| Geroch Group | p. 292 |
| Stationary Black Holes | p. 302 |
| Spherically Symmetric Solutions | p. 306 |
| Uniqueness Theorems for Static Black Holes | p. 312 |
| Stationary, Axially Symmetric Black Holes | p. 314 |
| Acknowledgments | p. 316 |
| Non-linear ¿-Models and Symmetric Spaces | p. 316 |
| Non-compact Riemannian Symmetric Spaces | p. 316 |
| Pseudo-Riemannian Symmetric Spaces | p. 319 |
| Consistent Truncations | p. 319 |
| Structure of the Lie Algebra | p. 319 |
| Time-Independent Gravitational Fields | p. 325 |
| Introduction | p. 325 |
| Field Equations | p. 327 |
| Generalities | p. 327 |
| Axial Symmetry | p. 333 |
| Asymptotic Flatness: Lichnerowicz Theorems | p. 334 |
| Newtonian Limit | p. 339 |
| Existence Issues and the Newtonian Limit | p. 340 |
| Far Fields | p. 341 |
| Far-Field Expansions | p. 341 |
| Conformal Treatment of Infinity, Multipole Moments | p. 344 |
| Global Rotating Solutions | p. 350 |
| Lindblom's Theorem | p. 350 |
| Existence of Stationary Rotating Axi-symmetric Fluid Bodies | p. 353 |
| The Neugebauer-Meinel Disk | p. 357 |
| Global Non-rotating Solutions | p. 360 |
| Elastic Static Bodies | p. 360 |
| Are Perfect Fluids O (3)-Symmetric? | p. 362 |
| Spherically Symmetric, Static Perfect Fluid Solutions | p. 365 |
| Spherically Symmetric, Static Einstein-Vlasov Solutions | p. 370 |
| Gravitational Lensing from a Geometric Viewpoint | p. 373 |
| Introduction | p. 373 |
| Some Basic Notions of Spacetime Geometry | p. 375 |
| Gravitational Lensing in Arbitrary Spacetimes | p. 378 |
| Conjugate Points and Cut Points | p. 381 |
| The Geometry of Light Cones | p. 385 |
| Citeria for Multiple Imaging | p. 391 |
| Fermat's Principle | p. 396 |
| Morse Index Theory for Fermat's Principle | p. 399 |
| Gravitational Lensing in Globally Hyperbolic Spacetimes | p. 403 |
| Criteria for Multiple Imaging in Globally Hyperbolic Spacetimes | p. 405 |
| Morse Theory in Globally Hyperbolic Spacetimes | p. 408 |
| Gravitational Lensing in Asymptotically Simple and Empty Spacetimes | p. 414 |
| References | p. 422 |
| Jürgen Ehlers - Bibliography | p. 427 |
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