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.

Keywords

Supergravity Models Integrable Equations in Physics Black Holes in String Theory Black Holes 
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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Italian Embassy in the Russian FederationMoscowRussia
  2. 2.Dipartimento di Fisica TeoricaUniversitá di Torino & INFN - Sezione di TorinoTorinoItaly
  3. 3.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchMoscow RegionRussia

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