Topology Change of Black Holes

The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological evolution can be understood as a handle attachment. It has been found that there are certain constraints on the nature of black hole topological evolution: (i) There are n kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii) Handles are further classified as either of black or white type, and only black handles appear in real black hole space-times. (iii) The spatial section of an exterior of the black hole region is always connected. As a corollary, it is shown that the formation of a black hole with an S**(n-2) x S**1 horizon from that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat space-times.