Analytical and Numerical Approaches to Mathematical Relativity / Edition 1

by Jïrg Frauendiener, Roger Penrose, Domenico J. W. Giulini, Volker Perlick

Overview

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 effects, including the emission of gravitational waves, are convincingly confirmed). Einstein’s tentative introduction, in 1917, of an additional term in his equations, specified 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 field (which had been only roughly confirmed 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.

Product Details

ISBN-13:	9783642068195
Publisher:	Springer Berlin Heidelberg
Publication date:	11/19/2010
Series:	Lecture Notes in Physics , #692
Edition description:	Softcover reprint of hardcover 1st ed. 2006
Pages:	281
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Differential Geometry and Differential Topology.- A 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.- Analytical Methods and Differential Equations.- Concepts of 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.- Numerical Methods.- 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.

Editorial Reviews

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)

From the Publisher