Existence and uniqueness of toric gravitational instantons
Conferences
Overview
Overview
abstract
Gravitational instantons are four-dimensional, non-compact, complete Ricci-flat Riemannian manifolds. Natural asymptotic conditions for these spaces include asymptotically flat (S^1 X R^3 with the flat metric), asymptotically locally Euclidean (ALE) and asymptotically Taub- NUT. I will discuss existence and uniqueness results for gravitational instatons admitting a torus symmetry. Solutions are characterised by data that encodes the fixed point sets of the torus action and for every admissible data there exists an instanton that is smooth up to possible conical singularities at the axes of symmetry. This leads to some qualitative differences with the analogous problem in the Lorentzian setting (i.e. stationary and axisymmetric vacuum black holes). I will also discuss generalisations to higher dimensions.
