A new picture shows Stephen Hawking among the guests at a barbecue during a conference sponsored by Epstein.

The March 2006 photograph, taken before Epstein was charged for unlawful sex with a minor, shows professor Hawking on the billionaire's private Caribbean island, Little St James, dubbed "the Island of Sin".

Hawking, currently the subject of Oscar-nominated film The Theory of Everything, also took a boat trip and a submarine tour, paid for by Epstein.

Eddie Redmayne plays Stephen Hawking in The Theory of Everything (Universal)

The trip was part of a science conference on neighbouring island St Thomas, which was paid for by Epstein, 61, and which 20 other internationally renowned scientists attended.

Epstein's island developed a reputation for depravity, and it is alleged that teenage girls were made to take part in orgies with on Little St James.