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Generating Geodesic Flows and Supergravity Solutions

  • Bergshoeff, E.
  • Chemissany, W.
  • Ploegh, A.
  • Trigiante, M.
  • Van Riet, T.
Published Article
Publication Date
Dec 14, 2016
Submission Date
Jun 13, 2008
DOI: 10.1016/j.nuclphysb.2008.10.023
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We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike $p$-brane solutions when they are lifted over a $p$-dimensional flat space. In particular, we consider the problem of constructing \emph{the minimal generating solution}: A geodesic with the minimal number of free parameters such that all other geodesics are generated through isometries. We give an intrinsic characterization of this solution in a wide class of orbits for various supergravities in different dimensions. We apply our method to three cases: (i) Einstein vacuum solutions, (ii) extreme and non-extreme D=4 black holes in N=8 supergravity and their relation to N=2 STU black holes and (iii) Euclidean wormholes in $D\geq 3$. In case (iii) we present an easy and general criterium for the existence of regular wormholes for a given scalar coset.

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