Abstract
It is shown that in many of the possible cases local null rotation invariance of the curvature and its first derivatives is sufficient to ensure that there is an isometry group G_r with rge 3 acting on (a neighbourhood of) the spacetime and containing a null rotation isotropy. The exceptions where invariance of the second derivatives is additionally required to ensure this conclusion are Petrov type N Einstein spacetimes, spacetimes containing “pure radiation” (a Ricci tensor of Segre type [(11,2)]), and conformally flat spacetimes with a Ricci tensor of Segre type [1(11,1)] (a “tachyon fluid”).
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