The way Jarmusch portrays the lives they lead, he's obviously interested in what day to day immortality would feel like and what it would do to someone, both emotionally and spiritually. Adam seems to be wishing his time would end, while Eve takes whatever sensual and tactile pleasures she can from the small things, like dancing. Adam has only one real connection to the outside world, a young local guy named Ian (Anton Yelchin), and other than that, he seems happy to hide from the world, writing and recording music that is for him, that's not really meant for an audience. Hiddleston seems perfectly suited for this role, and he pulls off that particular Jarmusch trick of delivering some great laugh lines without ever telegraphing a joke or dropping the morose exterior. If they ever get around to turning Neil Gaiman's "Sandman" into a film, Hiddleston is the only man for the job at this point, and Adam appears to have stepped out of the pages of that book.
Read more at Review: Tom Hiddleston and Tilda Swinton shine in Jim Jarmuschs moody Only Lovers Left Alive