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Supergravity black holes and billiards and the Liouville integrable structure associated with Borel algebras

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Abstract

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 \(\mathbb{B}_{\mathbb N} \) 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 \(\{\mathfrak{h}_{\alpha}\} \) 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.

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Authors and Affiliations

  1. Italian Embassy in the Russian Federation, Denezhny Pereulok, 5, 121002, Moscow, Russia

    Pietro Fré

  2. Dipartimento di Fisica Teorica, Universitá di Torino & INFN - Sezione di Torino, via P. Giuria 1, I-10125, Torino, Italy

    Pietro Fré

  3. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Moscow Region, Russia

    Alexander S. Sorin

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  1. Pietro Fré
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Correspondence to Pietro Fré.

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Fré, P., Sorin, A.S. Supergravity black holes and billiards and the Liouville integrable structure associated with Borel algebras. J. High Energ. Phys. 2010, 66 (2010). https://doi.org/10.1007/JHEP03(2010)066

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