The Conformal Structure of Space-Time: Geometry, Analysis, Numerics

Helmut Friedrich (auth.), Jörg Frauendiener, Helmut Friedrich (eds.)3540442804, 9783540442806

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.

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Table of contents :
Conformal Einstein Evolution….Pages 1-50
Some Global Results for Asymptotically Simple Space-Times….Pages 51-60
Black Holes….Pages 61-102
Conformal Geometry, Differential Equations and Associated Transformations….Pages 103-112
Twistor Geometry of Conformal Infinity….Pages 113-121
Isotropic Cosmological Singularities….Pages 123-134
Polyhomogeneous Expansions Close to Null and Spatial Infinity….Pages 135-159
Asymptotically Flat and Regular Cauchy Data….Pages 161-181
Construction of Hyperboloidal Initial Data….Pages 183-194
Exploring the Conformal Constraint Equations….Pages 195-222
Criteria for (In)finite Extent of Static Perfect Fluids….Pages 223-237
Problems and Successes in the Numerical Approach to the Conformal Field Equations….Pages 239-259
Some Aspects of the Numerical Treatment of the Conformal Field Equations….Pages 261-282
Data for the Numerical Calculation of the Kruskal Space-Time….Pages 283-295
Numerics of the Characteristic Formulation in Bondi Variables. Where We Are and What Lies Ahead….Pages 297-312
Numerical Experiments at Null Infinity….Pages 313-326
Local Characteristic Algorithms for Relativistic Hydrodynamics….Pages 327-348
Simulations of Generic Singularities in Harmonic Coordinates….Pages 349-358
Some Mathematical and Numerical Questions Connected with First and Second Order Time-Dependent Systems of Partial Differential Equations….Pages 359-370