Bases of Numerical Relativity
- Introduction
- Basic Differential Geometry
- Introduction
- Differentiable Manifolds
- Notion of Manifold
- Vectors on a Manifold
- Geometry of Hypersurfaces
- Geometry of Foliations
- Decomposition of Einstein Equation
- 3+1 Equations for Matter and Electromagnetic Field.
- Conformal Decomposition
- Asymptotic Flatness and Global Quantities
- The Initial Data Problem
- Choice of Foliation and Spatial Coordinates
- Evolution schemes
- Introduction
- Constrained Schemes
- Free Evolution Schemes
- Definition and Framework
- Propagation of the Constraints
- Constraint-Violating Modes
- Symmetric Hyperbolic Formulations