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Full Description
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.
Contents
Color Plates.- I: Numerics.- 1. Numerical Relativity and Black-Hole Collisions.- 2. Four Lectures on Numerical Relativity.- 3. Alternatives to Finite Difference Methods in Numerical Relativity.- 4. Temporal and Spatial Foliations of Spacetimes.- 5. Rotating and Oscillating Neutron Stars.- 6. Rotating Boson Stars.- 7. Numerical Investigation of Cosmological Singularities.- II: Computer Algebra.- 8. Overview of Computer Algebra in Relativity.- 9. Two-Loop Quantum Gravity with the Computer Algebra Program FORM.- 10. The Mathematic Packages CARTAN and MathTensor for Tensor Analysis.- 11. A Quadratic Curvature Lagrangian of Paw?owski and Raczka: A Finger Exercise with MathTensor.- 12. The Program CRACK for Solving PDEs in General Relativity.- 13. Algebraic Programming in the Hamiltonian Version of General Relativity.- 14. Causal Structure and Integrability in Moving Frames with Reduce.- III: Visualization.- 15. Four Lectures on Computer Graphics and Dkta Visualization.- 16. Visualization in Curved Spacetimes. I. Visualization of Objects via Four-Dimensional Ray-Tracing.- 17. Visualization in Curved Spacetimes. II. Visualization of Surfaces via Embedding.- IV: Exotica.- 18. Exotic Smoothness on Spacetime.- List of Figures.- List of Tables.
