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Can space exist without time, time without space, black holes without either?

As an aside, theoretical physicists love to play with fictitious arrangements of space and time - for example one dimension of space and one of time makes nice little diagrams and is one of the favorites. Undoubtedly people have investigated spaces with no time, and "spaces" with just time and no space, but I cannot see any practical use for them. Having both space and time makes things interesting (motion makes no sense without both, for example). Black holes probably can exist without time, but where would one be if there was no space?

Arthur Smith

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