Frauendiener J., Guilini D., Perlick V. (eds.) Analytical and numerical approaches to mathematical relativity (LNP692, Springer, 2006)(290s)_PGr_.pdf

Lecture Notes in Physics

Editorial Board

R. Beig, Wien, Austria

W. Beiglböck, Heidelberg, Germany

W. Domcke, Garching, Germany

B.-G. Englert, Singapore

U. Frisch, Nice, France

P. Hänggi, Augsburg, Germany

G. Hasinger, Garching, Germany

K. Hepp, Zürich, Switzerland

W. Hillebrandt, Garching, Germany

D. Imboden, Zürich, Switzerland

R. L. Jaffe, Cambridge, MA, USA

R. Lipowsky, Golm, Germany

H. v. Löhneysen, Karlsruhe, Germany

I. Ojima, Kyoto, Japan

D. Sornette, Nice, France, and Zürich, Switzerland

S. Theisen, Golm, Germany

W. Weise, Garching, Germany

J. Wess, München, Germany

J. Zittartz, Köln, Germany

The Lecture Notes in Physics

The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments

in physics research and teaching – quickly and informally, but with a high quality and

the explicit aim to summarize and communicate current knowledge in an accessible way.

Books published in this series are conceived as bridging material between advanced grad-

uate textbooks and the forefront of research to serve the following purposes:

• to be a compact and modern up-to-date source of reference on a well-deﬁned topic;

•

to serve as an accessible introduction to the ﬁeld to postgraduate students and nonspe-

cialist researchers from related areas;

•

to be a source of advanced teaching material for specialized seminars, courses and

schools.

Both monographs and multi-author volumes will be considered for publication. Edited

volumes should, however, consist of a very limited number of contributions only. Pro-

ceedings will not be considered for LNP.

Volumes published in LNP are disseminated both in print and in electronic formats,

the electronic archive is available at springerlink.com. The series content is indexed,

abstracted and referenced by many abstracting and information services, bibliographic

networks, subscription agencies, library networks, and consortia.

Proposals should be sent to a member of the Editorial Board, or directly to the managing

editor at Springer:

Dr. Christian Caron

Springer Heidelberg

Physics Editorial Department I

Tiergartenstrasse 17

69121 Heidelberg/Germany

christian.caron@springer-sbm.com

Jörg Frauendiener

Domenico J.W. Giulini

Volker Perlick

(Eds.)

Analytical and Numerical

Approaches to

Mathematical Relativity

With a Foreword by Roger Penrose

ABC

Editors

Jörg Frauendiener

Institut für Theoretische Astrophysik

Universität Tübingen

Auf der Morgenstelle 10

72076 Tübingen, Germany

E-mail: joergf@tat.physik.uni-

tuebingen.de

Volker Perlick

Institut für Theoretische Physik

TU Berlin

Hardenbergstrasse 36

10623 Berlin

E-mail: vper0433@itp.physik.tu-

berlin.de

Domenico J.W. Giulini

Fakultät für Physik und Mathematik

Universität Freiburg

Hermann-Herder-Str. 3

79104 Freiburg, Germany

E-mail: giulini@physik.uni-freiburg.de

J. Frauendiener et al., Analytical and Numerical Approaches to Mathematical Relativity ,

Lect. Notes Phys. 692 (Springer, Berlin Heidelberg 2006), DOI 10.1007/b11550259

Library of Congress Control Number: 2005937899

ISSN 0075-8450

ISBN-10

3-540-31027-4 Springer Berlin Heidelberg New York

ISBN-13

978-3-540-31027-3 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is

concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,

reproduction on microﬁlm or in any other way, and storage in data banks. Duplication of this publication

or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,

1965, in its current version, and permission for use must always be obtained from Springer. Violations are

liable for prosecution under the German Copyright Law.

Springer is a part of Springer Science+Business Media

springer.com

c Springer-Verlag Berlin Heidelberg 2006

Printed in The Netherlands

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,

even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws

and regulations and therefore free for general use.

Typesetting: by the authors and TechBooks using a Springer L A T E X macro package

Printed on acid-free paper

SPIN: 11550259

54/TechBooks

543210

Foreword

The general theory of relativity, as formulated by Albert Einstein in 1915,

provided an astoundingly original perspective on the physical nature of grav-

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, provid-

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 dif-

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”, ap-

pears now to be observationally demanded, and with this term included, 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

solar eclipse measurements at the Island of Principe in 1919, but which is now

very well established) has become an important tool in observational cosmol-

ogy, where gravitational lensing now provides a unique and direct means of

measuring the mass of very distant objects.

But long before general relativity and cosmology had acquired this im-

pressive observational status, these areas had provided a proliﬁc source of

mathematical inspiration, particularly in diﬀerential geometry and the the-

ory of partial diﬀerential equations (where sometimes this had been applied

to situations in which the number of space-time dimensions diﬀers from the

four of direct application to our observed space-time continuum). As we see

from several of the articles in this book, there is still much activity in all

these mathematical areas, in addition to other areas which have acquired

importance more recently. Most particularly, the interest in black holes, with

their horizons, their singularities, and their various other remarkable proper-

ties, both theoretical and in relation to observed highly dramatic astronom-

ical phenomena, has also stimulated much important research. Some have

interesting mathematical implications, involving particular types of mathe-

matical argumentations, such as the involvement of diﬀerential topology and

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: