  Self-duality in Euclidean gravitational set ups is a tool for finding
remarkable geometries in four dimensions. From a holographic perspective,
self-duality sets an algebraic relationship between two a priori independent
boundary data: the boundary energy-momentum tensor and the boundary Cotton
tensor. This relationship, which can be viewed as resulting from a topological
mass term for gravity boundary dynamics, survives under the Lorentzian
signature and provides a tool for generating exact bulk Einstein spaces
carrying, among others, nut charge. In turn, the holographic analysis exhibits
perfect-fluid-like equilibrium states and the presence of non-trivial vorticity
allows to show that infinite number of transport coefficients vanish.
