Ulm 2004 – scientific programme

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PV: Plenarvorträge

PV X

PV X: Plenary Talk

Wednesday, March 17, 2004, 11:30–12:30, H22

Cosmological Billiards — •Hermann Nicolai — Max Planck Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany

The dynamics of the Einstein-dilaton-p-form system in the vicinity of a spacelike singularity can be asymptotically described, at a generic spatial point, as a billiard motion in a region of Lobachevskii space (realized as an hyperboloid in the space of logarithmic scale factors). This is most conveniently done within the Hamiltonian formalism, and for an arbitrary number of spacetime dimensions D>3. A key role in the derivation is played by the Iwasawa decomposition of the spatial metric, which allows a separation of the degrees of freedom exhibiting an oscillatory or singular behavior from those that get “asymptotically frozen” as one approaches the singularity. There exists an intriguing link between the BKL analysis and certain indefinite Kac Moody algebras, hinting a the existence of a vast extension of the Geroch group in gravity and supergravity theories.