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zankaon
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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?
zankaon said: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?
zankaon said: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?
zankaon said:If one considered an idealized spherical expansion (of say neutrinos) for a patch of manifold outside a BH
zankaon said:then one could consider such expansion to be finite, bounded (in an orthogonal to the 2-surface) sense,
zankaon said: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 the same topological description, but in an environment becoming more extreme; hence the same manifold (continuum i.e. same inbetweenness).
zankaon said: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 (in an orthogonal to the 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 the same topological description, but in an environment becoming more extreme; hence the same manifold (continuum i.e. same inbetweenness). But yet does one have a construct (BH_h) interspersed between such 2 environments, but with a different topology? Topology commentary is always appreciated.
zankaon said:The ending answer would seem to be no.
zankaon said:For example if a larger BH coalesced with a smaller BH, the former would enlarge. Hence an expansion orthogonal to BH_h. So therefore such expansion (orthogonal to surface) of BH_h would be finite, bounded and thus not closed.
If you haven't read the popular book by Wald, Space, Time, and Gravity, University of Chicago Press, 1977, you would enjoy it!
I have no idea what you seem to be asserting about what happens to the horizon of a black hole when it coalesces with a smaller hole, but it doesn't sound right. To mention just one point, the horizon isn't a physical membrane but an abstract "teleologically defined" surface. At an event on the horizon, nothing in particular happens compared with nearby events, in terms of local physics.
The topology outside a black hole is typically spherical, meaning that the space around the black hole curves in all directions towards the center. This is due to the extreme gravitational pull of the black hole.
The topology inside a black hole is still a topic of debate and research. Some theories suggest that the space inside a black hole is infinitely curved and leads to a singularity, while others propose that it may be a wormhole connecting to another part of the universe.
Yes, we can indirectly observe the topology outside a black hole through its effects on surrounding objects, such as the distortion of light and the movement of matter. However, due to the strong gravitational pull, direct observation is currently impossible.
No, the topology outside a black hole can vary depending on the size and properties of the black hole. For example, a spinning black hole may have a different topology than a non-spinning one. Additionally, the presence of other objects or matter nearby can also affect the topology.
The topology outside a black hole plays a crucial role in determining its behavior, such as its gravitational pull, the formation of accretion disks, and the distortion of spacetime. It also affects the way it interacts with surrounding matter and objects.