Evanescent ergosurfaces and ambipolar hyperk\"ahler metrics

TL;DR

This paper explores the structure of supersymmetric 5d supergravity solutions featuring evanescent ergosurfaces, introducing a new class of ambipolar hyperk"ahler manifolds and providing an initial value construction method.

Contribution

It defines ambipolar hyperk"ahler manifolds, generalizes folded hyperk"ahler structures, and develops an initial value approach for constructing supersymmetric solutions with evanescent ergosurfaces.

Findings

Characterization of hyperk"ahler degeneration at the hypersurface

Construction of ambipolar hyperk"ahler manifolds from initial data

Initial value formulation for supersymmetric 5d supergravity solutions

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 hyperk\"ahler `base space' of such a solution is `ambipolar', changing signature from $(++++)$ to $(----)$ across a hypersurface. In this paper, we determine how the hyperk\"ahler structure must degenerate at the hypersurface in order for the 5d solution to remain smooth. This leads us to a definition of an ambipolar hyperk\"ahler manifold which generalizes the recently-defined notion of a `folded' hyperk\"ahler 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.