  We study the relations between all the vacua of Lorentzian and Euclidean
d=4,5,6 SUGRAs with 8 supercharges, finding a new limiting procedure that takes
us from the over-rotating near-horizon BMPV black hole to the Godel spacetime.
The timelike compactification of the maximally supersymmetric Godel solution of
N=1,d=5 SUGRA gives a maximally supersymmetric solution of pure Euclidean
N=2,d=4 with flat space but non-trivial anti-selfdual vector field flux
(``flacuum'') that, on the one hand, can be interpreted as an U(1) instanton on
the 4-torus and that, on the other hand, coincides with the graviphoton
background shown by Berkovits and Seiberg to produce the C-deformation
introduced recently by Ooguri and Vafa. We construct flacuum solutions in other
theories such as Euclidean type IIA supergravity.
