Frauendiener J., Giulini D.J.W., Perlick V. (Eds.). Analytical and numerical approaches to mathematical relativity

Springer, Berlin, New York, 2006, 296 pp. - ISBN10: 3-540-31027-4
The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gravitation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time. Now, some 90 years later, this extraordinary theory stands in superb agreement with observation, providing a profound accord between the theory and the actual physical behavior of astronomical bodies, which sometimes attains a phenomenal precision (in one case to about one part in one hundred million million, where several different non-Newtonian effects, including the emission of gravitational waves, are convincingly confirmed).Part I Differential Geometry and Differential Topology
A Personal Perspective on Global Lorentzian Geometry – (P.E. Ehrlich).
The Space of Null Geodesics (and a New Causal Boundary) – (R.J. Low).
Some Variational Problems in Semi-Riemannian Geometry – (A. Masiello).
On the Geometry of pp-Wave Type Spacetimes – (J.L. Flores and M. S.anchez).
Part II Analytical Methods and Differential Equations.
Concepts of Hyperbolicity and Relativistic Continuum Mechanics – (R. Beig).
Elliptic Systems – (S. Dain).
Mathematical Properties of Cosmological Models with Accelerated Expansion – (A.D. Rendall)
The Poincare Structure and the Centre-of-Mass of Asymptotically Flat Spacetimes – (L.B. Szabados).
Part III Numerical Methods.
Computer Simulation – a Tool for Mathematical Relativity – and Vice Versa – (B.K. Berger).
On Boundary Conditions for the Einstein Equations – (S. Frittelli and R. Gomez).
Recent Analytical and Numerical Techniques Applied to the Einstein Equations – (D. Neilsen, L. Lehner, O. Sarbach and M. Tiglio).
Some Mathematical Problems in Numerical Relativity – (M. Babiuc, B. Szil.agyi, J. Winicour).