Two special classes of space-times admitting a non-null valence two Killing spinor

Details Two special classes of space-times admitting a non-null valence two Killing spinor Two special classes of space-times admitting a non-null valence two Killing spinor

2009-08-11

arxiv.org/abs/0908.1463v4

Class.Quant.Grav.27:015004,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages; typos corrected, complex transfo added, references added

Scientific paper

10.1088/0264-9381/27/1/015004

Non-conformally flat space-times admitting a non-null Killing spinor of valence two are investigated in the Geroch-Held-Penrose formalism. Contrary to popular belief these space-times are not all explicitly known. It is shown that the standard construction hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations, KS1 and KS2, for the spin coefficients and the components of the Ricci spinor. An exhaustive list of (conformal classes of) space-times, in which either KS1 or KS2 are violated, is presented. The resulting space-times are each other's Sachs transforms, in general admit no Killing vectors and are characterized by a single arbitrary function.

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