“Discussed with Elon and, in light of beautiful Arcadia’s birthday, we felt it was better to also just share directly about our wonderful and incredible son Seldon Lycurgus,” 38-year-old Ms Zilis wrote.

“Built like a juggernaut, with a solid heart of gold. Love him so much,” she wrote. Mr Musk responded with a heart emoji.

The founder of SpaceX and Tesla believes that humanity is at risk from declining birth rates and has signalled his intention to have a large number of children.

“Bravo to big families,” the 53-year-old billionaire said three years ago. He has described falling birth rates as “the biggest danger civilisation faces by far.”

His offspring have been born to at least three different women: Ms Zilis; the Canadian electropop musician Grimes, whose real name is Claire Boucher; his ex-wife, author Justine Wilson; and, allegedly, with a glamorous young Maga influencer called Ashley St Clair, 26.