We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism tangent bundle. Such are examples non-Riemannian holonomy reduction, and (in complexified setting) appear in Bridgeland stability conditions moduli spaces Calabi-Yau three-folds. Using twistor methods we show that, dimension four - where there is connection wi...

Abstract We classify Einstein metrics on $$\mathbb {R}^4$$ R 4 invariant under a four-dimensional group of isometries including principal action the Heisenberg group. consider which are either Ricci-flat or negative Ricci curvature. show that all ...

A bstract We construct a cohomogeneity-1 helical black string in six-dimensional Einstein gravity. The solution branches from the onset of gravitational superradiant instability equal-spinning Myers-Perry string. isometry group is ℝ T × U(1) Z SU(2), where first two are isometries generated by linear combinations time translation, shifts along string, and rotation, each which individually broke...

We consider the critical behavior at the threshold of black-hole formation for the five-dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a d...

We consider the critical behavior at the threshold of black hole formation for the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a discre...