Stable topologies of the event horizon - art. no. 064006

In our previous work, it was shown that the topology of the event horizon ( TOEH) is determined by the past end points of the event horizon (EH). A tor oidal EH (coalescing EH) is related to a two-dimensional (one-dimensional) set of end points. Therefore, we can see the stability of the TOEH by exami ning the stability of the end points (caustics). In the present article, we examine the stability of the TOEH by the discussion of linear perturbation and catastrophe theory. We see that a simple case of a single spherical EH is unstable under the linear perturbation. Remarkably, it is newly conclud ed that an EH with handles (torus, double torus, etc.) is more probable tha n coalescencing EHs by the analysis of catastrophe theory. [S0556-2821(99)0 4004-7].