For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.

InhaltsangabeColor Plates.- I: Numerics.- 1. Numerical Relativity and Black-Hole Collisions.- 1. Astrophysical Motivation and Mathematical Formulation for Numerical Relativity.- 1.1 Overview and Motivation.- 1.2 Mathematical Formulation of the Equations.- 2. Numerical Techniques and Supercomputing.- 2.1 Finite Difference Techniques.- 2.2 Treating Elliptic Equations.- 2.3 Treating Evolution Equations.- 2.4 Testbeds and Convergence of Numerical Solutions.- 2.5 Coding and Parallel-Computing Issues.- 2.6 General Code Strategies.- 3. Black-Hole Initial-Data Sets, Tools for Analysis, and Techniques for Evolution.- 3.1 Basic Theory and Initial-Data Sets.- 3.2 Tools for Numerical Black-Hole Spacetimes.- 3.3 Evolution.- 4. Present Research Status in Black-Hole Studies.- 4.1 Spherical BH - 1D.- 4.2 Distorted BH - 2D.- 4.3 Rotating BH - 2D.- 4.4 Colliding BH - 2D.- 4.5 Black-Hole Horizon Studies.- 4.6 3D Black-Hole Studies.- References.- 2. Four Lectures on Numerical Relativity.- 1. The Causal Structure of Einstein's Field Equations.- 1.1 The Space-Plus-Time Decomposition.- 1.2 Invariant Algebraic Slicing.- 1.3 The Evolution System.- 1.4 Causal Structure of the Evolution System.- 2. First-Order Flux-Conservative Systems.- 2.1 Linear Systems.- 2.2 Nonlinear Systems.- 2.3 Einstein's Evolution Equations.- 3. Standard Numerical Methods.- 3.1 Flux-Conservative Equations.- 3.2 Boundary Conditions.- 3.3 Nonsmooth Data.- 4. Total Variation Diminishing Methods.- 4.1 Flux-Conservative Methods.- 4.2 The 1D Black-Hole Test.- References.- 3. Alternatives to Finite Difference Methods in Numerical Relativity.- 1. Introduction.- 2. The 3+1 Formalism.- 3. The Initial-Data Problem.- 3.1 Multiquadrics.- 3.2 Finite Elements.- 4. Matter Evolution in Curved Spacetimes.- 4.1 Particle-Mesh Methods.- 4.2 Smoothed Particle Hydrodynamics in Curved Space.- 5. Conclusions.- References.- 4. Temporal and Spatial Foliations of Spacetimes.- 1. Introduction.- 2. Time Slicings.- 2.1 Maximal Slicing.- 2.2 Harmonic Slicing.- 2.3 Results for the Oppenheimer-Snyder Spacetime.- 3. Spatial Foliations.- 3.1 Constant Mean Curvature Foliations.- 3.2 Examples of CMC Foliations.- References.- 5. Rotating and Oscillating Neutron Stars.- 1. Introduction: Nonrotating Neutron Stars.- 2. Rotating Neutron Stars.- 2.1 Basic Formulation.- 2.2 Numerical Solution Method.- 2.3 Results.- 3. Oscillations of Neutron Stars.- 3.1 Basic Formalism.- 3.2 Results for Quasinormal Mode Frequencies.- References.- 6. Rotating Boson Stars.- 1. Introduction.- 2. Field Equations.- 3. Spherically Symmetric Boson Star.- 4. Field Equations of a Rotating Boson Star.- 5. Particle Number, Mass, and Angular Momentum.- 6. Differential Rotation.- 7. Numerical Solution.- 8. Remarks.- References.- 7. Numerical Investigation of Cosmological Singularities.- 1. Introduction.- 2. Symplectic Methods.- 3. Mixmaster Model.- 4. Gowdy Model on T3 × R.- 5. U(1) Models.- 6. Conclusions.- References.- II: Computer Algebra.- 8. Overview of Computer Algebra in Relativity.- 1. Introduction.- 2. General-Purpose Systems.- 2.1 Computer Algebra.- 2.2 Modern Systems.- 2.3 Evaluation.- 2.4 Simplification.- 2.5 Programming.- 2.6 Data Types.- 3. General Relativity Systems.- 3.1 Requirements: Riemannian Geometry.- 3.2 Requirements: GR Library.- 3.3 Requirements: Generalizations and Applications.- 3.4 Efficiency.- 3.5 Dummy Indices.- 4. Applications.- 5. Summary.- References.- 9. Two-Loop Quantum Gravity with the Computer Algebra Program FORM.- 1. Introduction.- 2. Covariant Quantization of Gravity.- 2.1 Noncovariant Method.- 2.2 Covariant Method.- 3. FORM.- 3.1 Annotated Yang-Mills Program.- 3.2 Quantum Gravity.- References.- 10. The Mathematic Packages CARTAN and MathTensor for Tensor Analysis.- 1. Mathematica.- 1.1 The Front End.- 1.2 The Kernel.- 2. Tensor Calculations.- 3. CARTAN.- 3.1 General Features.- 3.2 A Charged Black Hole.- 3.3 A Spin-Polarized Cosmic String.- 4. MathTensor.- 4.1 Tensor Indices.- 4.2 Metric Variation of R2.- 4.3 Differential For