Alexander Skarsgard showed his chivalrous side, holding the car door open for Kate Bosworth as they left the Wiltern Theater after the Broken Bells concert in LA last night. Alexander was home in Stockholm, Sweden, just two days ago but hopped on a flight with his untied boots to take his lady out on the town. The two have been apart for much of the past few months while he filmed Battleship in Hawaii and stopped off in Germany. Kate, meanwhile, worked on one movie in Michigan and is gearing up for her next project. This week she also launched her new jewelry subscription website, where you fill out a personality quiz and Kate and her partner will send you pieces they think fit your taste. Still, there's always a free evening for a date with her handsome man, and yesterday a rock show was just the ticket.