Einsteinu27s Equations in Vacuum Spacetimes with Two Spacelinke Killing Vectors Using Affine Projection Tensor Geometry

摘要

Einsteinu27s equations in vacuum spacetimes with two spacelike killing vectors are explored using affine projection tensor geometry. By doing a semi-conformal transformation on the metric, a new u22fiducialu22 geometry is constructed using a projection tensor fields. This fiducial geometry provides coordinate independent information about the underlying structure of the spacetime without the use of an explicit form of the metric tensor.