GLOBAL STRUCTURE OF SUPERGRAVITY DOMAIN-WALL SPACE-TIMES

The supersymmetric supergravity domain wall space-times considered by Cvetic and Griffies and Rey are shown to be incomplete and extensions are provided, in detail in the case of type II walls. The extensions, which are not unique, are conformal to a portion to the Einstein cylinder with certain points removed. The presence of the domain wall may thus be said to close up the space. The extensions contain Cauchy horizons with zero surface gravity and provided one makes no identifications they are causal. The key to the extensions is the correct understanding of lorentzian horospheres. Because the domain walls are, in a certain sense, at the end of the universe there may be zero modes bound to the domain walls which are connected with the Dirac-Singleton representations of SO(3,2).