Regular Article - Theoretical Physics
On the six-dimensional Kerr theorem and twistor equation
Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco, 50670-901, Brazil
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Accepted: 7 April 2014
Published online: 29 April 2014
The Kerr theorem is revisited as part of the twistor program in six dimensions. The relationship between pure spinors and integrable 3-planes is investigated. The real condition for Lorentzian spacetimes is seen to induce a projective property in the space of solutions, reminiscent of the quaternionic structure of the six-dimensional Lorentz group. The twistor equation (or Killing spinor equations generically) also has an interpretation as integrable null planes, and a family of Einstein spacetimes with this property are presented in the Kerr–Schild fashion.
© SIF and Springer-Verlag Berlin Heidelberg, 2014