The relationship between Natalie and her father Avner Hershlag is said to be ‘very frosty’ since he became aware of her on-screen lesbian romp.
The 29-year-old actress plays a ballerina in a New York City ballet company, who is obsessed in taking the lead role in Swan Lake.
But when she faces competition from a new dancer, played by Mila Kunis, their rivalry turns sexual.
A source told the Daily Mail: ‘Natalie is a very private and dignified person and is often influenced by her father’s approval.
‘This, however, was one role she simply didn’t want to turn down even though she knew it would upset her father.
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‘He still sees her as a baby and always will and thinks showing herself like this is degrading. Things are frosty between them right now.’
Despite angering her dad, Black Swan’s director Darren Aronosfsky has said that Natalie deserves an Oscar for her performance.
Speaking at the BFI London Film Festival, he said: ‘I gave Natalie a good opportunity I think and she was cast well and she really did the work.
‘She spent 12 months studying ballet and becoming a dance. I think that physical workout really mentally got her there.