25 research outputs found
On exact solutions in multidimensional gravity with antisymmetric forms
This short review deals with a multidimensional gravitational model
containing dilatonic scalar fields and antisymmetric forms. The manifold is
chosen in the product form. The sigma-model approach and exact solutions are
reviewed.Comment: 22 pages, Latex, to be published in Proc. of E. Majorana School on
Gravitation and Cosmology (30 April - 10 May 2003, Erice
Stable exponential cosmological solutions with zero variation of G in the Einstein–Gauss–Bonnet model with a Λ -term
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
Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras
In this paper we show that the supergravity equations describing both cosmic
billiards and a large class of black-holes are, generically, both Liouville
integrable as a consequence of the same universal mechanism. This latter is
provided by the Liouville integrable Poissonian structure existing on the dual
Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive
the explicit integration algorithm associated with all symmetric spaces U/H^{*}
relevant to the description of time-like and space-like p-branes. The most
important consequence of our approach is the explicit construction of a
complete set of conserved involutive hamiltonians h_{\alpha} that are
responsible for integrability and provide a new tool to classify flows and
orbits. We believe that these will prove a very important new tool in the
analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two references
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