Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

Simulation des Spannungs- und Verformungsverhaltens von leichtbaurelevanten Stahlblech-Mehrschichtverbunden (StMV). T. 1: Strukturmechanische Charakterisierung von Stahlblech-Mehrschichtverbunden. T. 2: Simulation von Stahlblech-Mehrschichtverbunden am Beispiel der Reserveradmuldenabdeckung des VW Golf Variant

Available from TIB Hannover: RR 7808(343) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEStifterverband fuer die Deutsche Wissenschaft e.V., Essen (Germany). Stiftung StahlanwendungsforschungDEGerman

Gestaltung mechanischer Schnittstellen im Baukasten Mikrosystemtechnik am Beispiel miniaturisierter Linearversteller (BAULIN) Abschlussbericht

Available from TIB Hannover: F04B1309 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Bildung und Forschung (BMBF), Bonn (Germany)DEGerman