On algebraically special vacuum spacetimes in five dimensions

Understand

Vacuum solutions admitting a hypersurface-orthogonal repeated principal null direction are an important class of 4d algebraically special spacetimes.

• We investigate the 5d analogues of such solutions: vacuum spacetimes admitting a hypersurface-orthogonal multiple Weyl aligned null direction (WAND).
• Such spacetimes fall into 4 families determined by the rank of the 3X3 matrix that defines the expansion and shear of the multiple WAND.
• The rank 3 and rank 0 cases have been studied previously.