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He constructed it after the War of the Alliance to destroy Arnor
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There is a theory, based on the Dwarvish name, that Carn-dum was an abandoned Dwarven settlement that the Witch-king reinhabited and turned into his capital.
Aside from the linguistic connection (primarily resting on the "-dum" ending) it is unsubstantiated, but it seems plausible and I like to believe it.