Kate Bosworth and Michael Polish Keep Close in Sydney

Kate Bosworth and Michael Polish had their arms around each other yesterday at Sydney Airport. Kate tweeted that she was heading Down Under on a flight, and Michael responded by sharing a picture emblazoned with the phrase "Under the same sky, dreaming the same dream." The couple was back out exploring Australia together today.

Kate officially announced her engagement to Michael last month. Kate and Michael, a director, met while making the movie Big Sur together. They stepped out in public as a pair for the first time at a Coldplay concert a little more than a year ago, shortly after Kate and her former True Blood beau, Alexander Skarsgard, parted ways. Since then, Kate and Michael have been nearly inseparable, and the to-be-married couple is frequently seen out on low-key dates in LA, as well as side by side at star-studded events including film festivals, Coachella, and New York Fashion Week.