N=4 BPS black holes and octonionic twistors

TL;DR

This paper extends the geometric description of BPS black holes in supergravity by relating 1/4-BPS solutions to holomorphic curves on a new octonionic twistor space, broadening the mathematical framework for understanding extremal black holes.

Contribution

It generalizes the twistor space approach from N=2 to N=4 supergravity, introducing an octonionic structure for describing 1/4-BPS black holes.

Findings

Holomorphic curves on a new twistor space correspond to 1/4-BPS black holes.

Provides a geometric framework for potential new solutions.

Generalizes quaternionic to octonionic structures in supergravity.

Abstract

Stationary, spherically symmetric solutions of N=2 supergravity in 3+1 dimensions have been shown to correspond to holomorphic curves on the twistor space of the quaternionic-K\"ahler 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 N=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,n_v+2)/SO(8)xSO(n_v+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.