Description
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. Conformal Einstein Evolution.- Some Global Results for Asymptotically Simple Space-Times.- Black Holes.- Conformal Geometry, Differential Equations and Associated Transformations.- Twistor Geometry of Conformal Infinity.- Isotropic Cosmological Singularities.- Polyhomogeneous Expansions Close to Null and Spatial Infinity.- Asymptotically Flat and Regular Cauchy Data.- Construction of Hyperboloidal Initial Data.- Exploring the Conformal Constraint Equations.- Criteria for (In)finite Extent of Static Perfect Fluids.- Problems and Successes in the Numerical Approach to the Conformal Field Equations.- Some Aspects of the Numerical Treatment of the Conformal Field Equations.- Data for the Numerical Calculation of the Kruskal Space-Time.- Numerics of the Characteristic Formulation in Bondi Variables. Where We Are and What Lies Ahead.- Numerical Experiments at Null Infinity.- Local Characteristic Algorithms for Relativistic Hydrodynamics.- Simulations of Generic Singularities in Harmonic Coordinates.- Some Mathematical and Numerical Questions Connected with First and Second Order Time-Dependent Systems of Partial Differential Equations.
