  A class of black objects which are solutions of pure gravity with negative
cosmological constant are classified through the mapping between the Killing
spinors of the ground state and those of the transverse section. It is shown
that these geometries must have transverse sections of constant curvature for
spacetime dimensions d below seven. For d > 6, the transverse sections can also
be Euclidean Einstein manifolds. In even dimensions, spacetimes with transverse
section of nonconstant curvature exist only in d = 8 and 10. This
classification goes beyond standard supergravity and the eleven dimensional
case is analyzed. It is shown that if the transverse section has negative
scalar curvature, only extended objects can have a supersymmetric ground state.
In that case, some solutions are explicitly found whose ground state resembles
a wormhole.
