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Title

MAXIMAL ACHRONAL BOUNDARIES

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Abstract

 ACCORDING TO A THEOREM BY PENROSE AN ACHRONAL BOUNDARY B SPLITS THE SPACE-TIME INTO 3 DISJOINT SETS. B ITSELF, A PAST SET P AND A FUTURE SET F SUCH THAT ¶P=¶F=B. IN MINKOWSKI SPACE-TIME IT ALWAYS TURNS OUT THAT F=I+(B) AND P=I-(B).BUT THIS NEED NOT HOLD FOR ALL SPACES. HERE WE SHOW THAT THE NECESSARY AND SUFFICIENT CONDITION FOR THIS EQUATION TO HOLD IS THAT B BE A MAXIMAL ACHRONAL BOUNDARY.

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