Abstract
A new family of euclidean Einstein metrics with self-dual Weyl tensor have been obtained using ideas from extended supersymmetries1,2. The basic supersymmetric formalism3, known as harmonic superspace, was adapted to the computation of self-dual Einstein metrics in 4. The resulting metric depends on 4 parameters besides the Einstein constant and has for isometry group U(1) × U(1), with hypersurface generating Killing vectors. In the limit of vanishing Einstein constant we recover a family of hyperkähler metrics within the Multicentre family 5 (in fact the most general one with two centres). Our results include the metrics of Plebanski and Demianski6 when these ones are restricted to be self-dual Weyl. From Flaherty's equivalence 7 these metrics can also be interpreted as a solution of the coupled Einstein-Maxwell field equations, for which we have given the Maxwell field strength forms2.
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