Generating Geodesic Flows and Supergravity Solutions

TL;DR

This paper studies geodesic solutions in supergravity moduli spaces, identifying minimal generating solutions and applying the approach to black holes, vacuum solutions, and wormholes across various dimensions.

Contribution

It introduces an intrinsic characterization of minimal geodesic solutions in supergravity moduli spaces, applicable to diverse cases including black holes and wormholes.

Findings

Characterization of minimal geodesic solutions in supergravity

Application to D=4 black holes and their relations

Criteria for regular Euclidean wormholes

Abstract

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.