The generic condition is generic
Abstract
We consider the generic condition for vectors—both null and nonnull—at a fixed pointp of a spacetime, and ask just how generic this condition is. In a general spacetime, if the curvature is not zero at the pointp, then the generic condition is found to be generic in the mathematical sense that it holds on an open dense set of vectors atp; more specifically, if there are as many as five nonnull vectors in general position atp which fail to satisfy the generic condition, then the curvature vanishes atp. If the Riemann tensor is restricted to special forms, then stronger statements hold: An Einstein spacetime with three linearly independent nongeneric timelike vectors atp is flat atp. A Petrov type D spacetime may not have any nongeneric timelike vectors except possibly those lying in the plane of the two principal null directions; if any of the nonnull vectors in such a plane are nongeneric, then so are all the vectors of that plane, as well as the plane orthogonal to it.
 Publication:

General Relativity and Gravitation
 Pub Date:
 September 1993
 DOI:
 10.1007/BF00759194
 Bibcode:
 1993GReGr..25..939B