If topology of a manifold were invariant (or not), what specifically would topology of a patch of such manifold in neighborhood (outside) of such BH, suggest?
If one considered an idealized spherical expansion (of say neutrinos) for a patch of manifold outside a BH; then one could consider such expansion to be finite, bounded (normal to 2-surface) sense, and hence such expansion per se would be not closed. Now if one considered the same gedanken simulation, but for less than BH_h (BH horizon), then the experiment in principle, would seem to have same topological description, but in an environment becoming more extreme; hence the same manifold (continuum i.e. same inbetweenness). Such BH_h construct between such 2 environments, would not seem then to relate to different topologies. Also can a patch of manifold suddenly appear when BH forms; or disappear after the Big Bang commences? Might ‘dark star’ construct allow for greater flexibility in such rendering? TMM