Monday, January 7, 2019

general relativity - Charged versus rotating black holes as different kinds of wormholes


I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to different exteriors that are merely isometric regions of spacetime.



Now I want to ignore whether that is correct. (So ignore the issue that differential geometry allows transition maps between local charts so you can obviously identify two sufficiently isometric regions by just connecting one to the other by appropriate transition maps.)


What I am interested in is what is the basis for a potentially infinitesimal amount of charge changing so fundamentally whether the isometric regions exterior to the black hole are the same universe or different universe?


Specifically, how would that happen, how could that happen? And to do it you might have to distinguish the two possibilities, which might require not ignoring the fact that you can clearly identify them.


But I am trying to ask how charge can do that? And how anything could do it? And what would required to assert the two isometric solutions are different? For instance if you look at the Penrose diagram you could just translate the diagram upwards and identify all the parts.




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