Time-like reductions of supergravity and black string solutions

• Main Author: Dempster, Paul
• Published: University of Liverpool 2014
• Subjects: 510
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.644366

We consider various geometrical and physical aspects of the supergravity q-maps, which are induced by dimensional reduction to three dimensions of five-dimensional N = 2 supergravity theories coupled to vector multiplets. In this way, the q-maps can be thought of as a composition of the r-maps and c-maps. We treat in parallel the case of reduction over two space-like directions and over one space-like and one time-like direction. We observe that in the latter case, surprisingly, the order in which the time-like and space-like reductions are performed is relevant for some geometrical properties of the resulting reduced theories. For the simplest example of pure supergravity in five dimensions, we show indeed that the target manifolds obtained from the two reductions correspond to inequivalent open submanifolds in the pseudo-Riemannian symmetric space G₂₍₂₎/(SL₂·SL₂). Moreover, each submanifold is endowed with a different integrable structure which makes one a complex manifold and the other a para-complex manifold. As an application we investigate how the q-map can be used to generate new non-extremal and extremal non-BPS static black string solutions in five dimensions. We also make progress towards constructing new stationary solutions. The generic nature of these constructions, which don't rely on the target manifolds being symmetric spaces, allow us to gain a more systematic understanding of various properties of black objects in supergravity.