TOPOLOGICAL APPEARANCE OF EVENT HORIZON - WHAT IS THE TOPOLOGY OF THEEVENT HORIZON THAT WE CAN SEE

The topology of the event horizon (TOEH) is usually believed to be a s phere. Nevertheless, some numerical simulations of gravitational colla pse with a toroidal event horizon or the collision of event horizons a re reported. Considering the indifferentiability of the event horizon (EH), we see that such non-trivial TOEHs are caused by the set of endp oints (the crease set) of the EH. The two-dimensional (one-dimensional ) crease set is related to the toroidal EH (the coalescence of the EH) . Furthermore, examining the stability of the structure of the endpoin ts, it becomes clear that the spherical TOEH is unstable under linear perturbation. On the other hand, a discussion based on catastrophe the ory reveals that the TOEH with handles is stable and generic. Also, th e relation between the TOEH and the hoop conjecture is discussed. It i s shown that the Kastor-Traschen solution is regarded as a good exampl e of the hoop conjecture by the discussion of its TOEH. We further con jecture that a non-trivial TOEH can be smoothed out by rough observati on in its mass scale.