The actress elaborated on her relationship status with the tech mogul in a new Instagram post on Tuesday.
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Amber Heard is opening up about her split from Elon Musk .

After initially announcing the breakup via an Instagram caption that said simply, “Put a fork in it,” the actress is now elaborating on her relationship status with the tech mogul in a follow-up post.

“Being in the public eye means having to explain yourself to so many people, so much of the time,” Heard wrote on Tuesday. “In this case, I’d like to remain more quiet. Although we have broken up, Elon and I care deeply for one another and remain close. Thank you for the continued support, respect, and privacy during these difficult, very human times.”

Musk broke his silence on the split in the comment section of Heard’s original “put a fork in it” Instagram post, writing, “V cute❤️.” He then added a lengthier response, writing, “Although Amber and I did break up, we are still friends, remain close and love one another.”

He added, “Long distance relationships, when both partners have intense work obligations are always difficult, but who knows what the future holds.”

A source confirmed the breakup news to PEOPLE on Monday, revealing that the two “are no longer dating.”

“They had fun for a few months, but are both very busy with work now. It was getting hard to find time to see each other,” the insider added, noting that Musk initiated the split.

“Elon is working day and night. This is his life and he loves it. He is in no position to be in a relationship right now and ended it.”

Dating rumors first began swirling last year when the actress and Musk were spotted out together several times amid their respective divorces — Heard’s contentious divorce from actor Johnny Depp was finalized in January and Musk filed for divorce from wife and Westworld actress Talulah Riley in January 2015.

The breakup comes as a shock, as the former couple were recently spotted out, both donning smiles, in Los Angeles in June. One month earlier, Heard and Musk spent some time Down Under while Heard filmed Aquaman.

Although they began spending time together after Heard’s divorce, the Tesla founder first took interest in Heard in 2013 when he appeared in Robert Rodriguez’s film Machete Kills.

“When the time was right and they were both single last year, he started pursuing her romantically,” a source previously told PEOPLE. “She was playing hard to get for a while, which made him even more interested.”