Evanescent ergosurfaces and ambipolar hyperkähler metrics

Abstract

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.