Analytical and Numerical Approaches to Mathematical Relativity

1. Front Matter

   Pages I-XVII

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2. Differential Geometry and Differential Topology

   1. Front Matter

      Pages I-XVII

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   2. A Personal Perspective on Global Lorentzian Geometry

      • Paul E. Ehrlich

      Pages 3-34

   3. The Space of Null Geodesics (and a New Causal Boundary)

      • Robert J. Low

      Pages 35-50

   4. Some Variational Problems in Semi-Riemannian Geometry

      • Antonio Masiello

      Pages 51-77

   5. On the Geometry of pp-Wave Type Spacetimes

      • José L. Flores, Miguel Sánchez

      Pages 79-98

3. Analytical Methods and Differential Equations

   1. Front Matter

      Pages I-XVII

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   2. Concepts of Hyperbolicity and Relativistic Continuum Mechanics

      • Robert Beig

      Pages 101-116

   3. Elliptic Systems

      • Sergio Dain

      Pages 117-139

   4. Mathematical Properties of Cosmological Models with Accelerated Expansion

      • Alan D. Rendall

      Pages 141-155

   5. The Poincaré Structure and the Centre-of-Mass of Asymptotically Flat Spacetimes

      • László B. Szabados

      Pages 157-184

4. Numerical Methods

   1. Front Matter

      Pages I-XVII

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   2. Computer Simulation – a Tool for Mathematical Relativity – and Vice Versa

      • Beverly K. Berger

      Pages 187-203

   3. On Boundary Conditions for the Einstein Equations

      • Simonetta Frittelli, Roberto Gómez

      Pages 205-222

   4. Recent Analytical and Numerical Techniques Applied to the Einstein Equations

      • Dave Neilsen, Luis Lehner, Olivier Sarbach, Manuel Tiglio

      Pages 223-249

   5. Some Mathematical Problems in Numerical Relativity

      • Maria Babiuc, Béla Szilágyi, Jeffrey Winicour

      Pages 251-274

5. Back Matter

   Pages 275-279

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The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, 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, prov- ing 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 d- ferent non-Newtonian e?ects, including the emission of gravitational waves, are convincingly con?rmed). Einstein’s tentative introduction, in 1917, of an additional term in his equations, speci?ed by a “cosmological constant”, - pearsnowtobeobservationallydemanded,andwiththistermincluded,there is no discrepancy known between Einstein’s theory and classical dynamical behavior, from meteors to matter distributions at the largest cosmological scales. One of Einstein’s famous theoretical predictions that light is bent in a gravitational ?eld (which had been only roughly con?rmed by Eddington’s solareclipsemeasurementsattheIslandofPrincipein1919,butwhichisnow very well established) has become an important tool in observational cosm- ogy, where gravitational lensing now provides a unique and direct means of measuring the mass of very distant objects.

• Relativity
• Riemannian geometry
• differential geometry
• general relativity
• mathematical relaivity
• numerical relativity

From the reviews:

"The 319th Wilhelm-and-Else-Heraeus Seminar ‘Mathematical Relativity: New Ideas and Developments’ took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume … . volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institution’s library purchases a copy!" (John M Stewart, Classical and Quantum Gravity, Issue 24, 2007)

• Institut für Theoretische Astrophysik, Universität Tübingen, Tübingen, Germany

  Jörg Frauendiener

• Fakultät für Physik und Mathematik, Universität Freiburg, Freiburg, Germany

  Domenico J.W. Giulini

• Institut für Theoretische Physik, TU Berlin, Berlin, Germany

  Volker Perlick

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