in string theory phenomenology the vacua of the theory that preserve supersymmetry typically involve products of four-dimensional Minkowski space with complicated manifolds such as Calabi-Yaus. In the supergravity approximation, and in the simplest cases with trivial fluxes and dilaton, the metric on the compact Calabi-Yau should be Ricci-flat, and such metrics are not known analytically. In general, finding four-dimensional Poincaré invariant vacua can be thought of as the problem of solving the Euclidean Einstein equation on the compactification manifold with specific matter. The Euclidean problem of finding Calabi-Yau metrics that are Ricci-flat has received attention recently, with an approach based on Ricci-flow [@Headrick:2005ch] and a spectral approach based on an algebraic representation of the metric [@Donaldson; @Douglas:2006rr; @Douglas:2006hz; @Braun:2008jp].[^2] However, these are fundamentally tied to working with Kähler geometries, and using the associated complex coordinates.

A natural question is then whether there exist numerical methods to find general stationary and static black holes in more than four dimensions, and to find solutions to the Euclidean Einstein equation such as those governing phenomenological vacuum compactifications in string theory. In these higher dimensional settings the dynamical numerical methods that are so well explored in four dimensions simply generalize. Thus in principle a 