2009/03/31 by Pietro Fré, Pietro Fre, Alexander S. Sorin
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #gr-qc #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/jhep03(2010)066
48 pages, 7 figures, LaTex; V1: misprints corrected, two references added
arxiv created 2009/11/01 · openalex publication_date 2010/03/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 BN of the simple Lie algebra AN-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 hα 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.