General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.
Table of ContentsA Personal Perspective on Global Lorentzian Geometry.- The Space of Null Geodesics (and a New Causal Boundary).- Some Variational Problems in Semi-Riemannian Geometry.- On the Geometry of pp-Wave type Spacetimes.- Concepts fo Hyperbolicity and Relativistic Continuum Mechanics.- Elliptic Systems.- Mathematical Properties of Cosmological Models With Accelerated Expansion.- The Poincaré Structure and the Centre-of-Mass of Asymptotically Flat Spacetimes.- Computer Simulation - a Tool For Mathematical Relativity - and Vice Versa.- On Boundary Conditions for the Einstein Equations.- Recent Analytical and Numerical Techniques Applied to the Einstein Equations.- Some Mathematical Problems in Numerical Relativity.