Abstract
Stationary, spherically symmetric solutions of 
= 2 supergravity
in 3+1 dimensions have been shown to correspond to holomorphic curves
on the twistor space of the quaternionic-Kähler space which arises in the
dimensional reduction along the time direction. In this note, we
generalize this result to the case of 1/4-BPS black holes in = 4
supergravity, and show that they too can be lifted to holomorphic curves
on a ``twistor space'' Z, obtained by fibering the Grassmannian F = SO(8)/U(4)
over the moduli space in three-dimensions SO(8, nv + 2)/SO(8) × SO(nv+2). This provides a kind of octonionic generalization
of the standard constructions in quaternionic geometry, and may be useful
for generalizing the known BPS black hole solutions, and finding new non-BPS
extremal solutions.
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