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"Anyway, sorry for being an idiot," he continued. "The radio silence hurts a lot. It only matters because I really like you."
In court yesterday one of Depp's lawyers, Eleanor Laws, pressed Heard about the messages, asking her, "Were you telling Mr Depp about this?"
"Time and again, you have accused [Depp] of being jealous, but we can see here you are in communication with someone," Laws said.
"I think all jealousy could be deemed illogical," claimed Heard.
Despite denying they had an affair while Heard was married to Depp, building concierge Alejandro Romero wrote in a sworn statement that he saw Musk "a few times a week" late at night.
He also stated that Musk "always visit when Mr Depp was not at home" from around 11 pm to midnight.
Heard responded: "He's wrong. I wasn't even in communication with Elon until 2016."
She said the pair were "friends at that moment. We had just become friends."
Heard said in a witness statement provided to the court that she was physically abused by Depp including being punched, slapped, kicked, head-butted and choked.
"He was always antagonised by shows of will, like me standing up after he had knocked me down. Often, especially earlier in the relationship, I wouldn't even block the blows; I would just freeze and disassociate."
Depp has brought a libel case against the publishers of The Sun and its executive editor, Dan Wootton, over an article which called him a "wife beater". Depp vehemently denies abusing Heard, however she maintains she was attacked by him on a number of occasions in drink- and drug-fuelled rages.
Tuesday morning's evidence centred around the days before Heard filed for divorce.