3+1 Formalism in General Relativity Bases of Numerical Relativity /

• Main Author: Gourgoulhon, Eric (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Series: Lecture Notes in Physics, 846
• Subjects: Physics.; Computer mathematics.; Gravitation.; Astronomy.; Astrophysics.; Cosmology.; Numerical and Computational Physics.; Classical and Quantum Gravitation, Relativity Theory.; Astronomy, Astrophysics and Cosmology.; Computational Mathematics and Numerical Analysis.

This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliatio...

Table of Contents:

• Basic Differential Geometry
• Geometry of Hypersurfaces
• Geometry of Foliations
• 3+1 decomposition of Einstein Equation
• 3+1 Equations for Matter and Electromagnetic Field
• Conformal Decompositon
• Asymptotic Flatness and Global Quantities
• The Initial Data Problem
• Choice of Foliation and Spatial Coordiinates
• Evolution Schemes
• Conformal Killing Operator and Conformal Vector Laplacian
• Sage Codes.