For the asymptotically flat spacetime, in accordance with (5), one has c = -3[pi]m/2b and
(I) Figures 2, 3, and 4 show the potential functions, temporal evolution of the gravitational perturbation, and quasinormal frequency obtained by WKB method in asymptotically flat spacetime.
(i) The form of the effective potential in dS spacetime is similar to that in asymptotically flat spacetime. Figure 5 indicates that, for given l and r, the effective potential decreases with increasing b; and for given b and r, it increases with increasing angular quantum number l.
Caption: FIGURE 2: The effective potential for odd parity gravitational perturbation in asymptotically flat spacetime, with [r.sub.h] = 1, l = 2 (a) and with [r.sub.h] = 1, b = 5 (b).
This first of two volumes of proceedings contains 19 technical papers on such topics as instabilities in kinetic theory and their relationship to the ergodic theorem, the uniqueness of photon spheres in static vacuum
asymptotically flat spacetimes, an initial-boundary value problem in a strip for two-dimensional equations of Zacharov-Kunzhetsov type, an extension of harmonicity and holomorphy, and over-determined transforms in integral geometry.
Thus, toroidal event horizons are only marginally prohibited when considering eternal black holes in
asymptotically flat spacetimes. However, if trapped surfaces cannot realistically form during gravitational collapse then topological censorship is bypassed entirely, leaving the toroidal dark hole (TDH) a viable possibility.