Generating Geodesic Flows and Supergravity Solutions

Details Generating Geodesic Flows and Supergravity Solutions Generating Geodesic Flows and Supergravity Solutions

2008-06-13

arxiv.org/abs/0806.2310v4

Nucl.Phys.B812:343-401,2009

Physics

High Energy Physics

High Energy Physics - Theory

Replaced by final version to appear in Nuclear Physics B, Replacement has very minor changes, major results unchanged

Scientific paper

10.1016/j.nuclphysb.2008.10.023

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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