Paper detail

Evanescent ergosurfaces and ambipolar hyperkähler metrics

A supersymmetric solution of 5d supergravity may admit an `evanescent ergosurface': a timelike hypersurface such that the canonical Killing vector field is timelike everywhere except on this hypersurface. The hyperkähler `base space' of such a solution is `ambipolar', changing signature from $(++++)$ to $(----)$ across a hypersurface. In this paper, we determine how the hyperkähler structure must degenerate at the hypersurface in order for the 5d solution to remain smooth. This leads us to a definition of an ambipolar hyperkähler manifold which generalizes the recently-defined notion of a `folded' hyperkähler manifold. We prove that such manifolds can be constructed from `initial' data prescribed on the hypersurface. We present an `initial value' construction of supersymmetric solutions of 5d supergravity, in which such solutions are determined by data prescribed on a timelike hypersurface, both for the generic case and for the case of an evanescent ergosurface.