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Melanotrypophobia, although the Greek term is "mayri trypa", literally "black hole".

Any relation to the words melancholy?

Yes, that is cognate with ancient Greek μελαγχολία, and with the same root: μέλας

Yes, as the sibling said, melancholy means "black bile".

Melanastrophobia, perhaps? "Black star phobia". I don't think a modern term has been coined for black holes from ancient Greek vocabulary.

Hypochondriac