J.J. Abrams has started production on his Star Trek sequel as planned, Paramount Pictures announced Tuesday.

Principal photography on the sci-fi film has begun in Los Angeles. Abrams previously said production would get under way January 12.

The film is due to hit theaters May 17, 2013. In November, Paramount Pictures bumped the release date from June 29, 2012, to May 17, 2013.

Meanwhile, speculation continues over the lead role that will be played by Benedict Cumberbatch, who joined the cast earlier this month.

It had previously been rumored that Cumberbatch would play the main villain, but in subsequent interviews, the actor and Abrams have both dropped hints that might not be the case.

In an MTV interview published Monday, Cumberbatch said it was just supposition that he would be playing the main villain. Benicio del Toro had also been rumored for the role.

The Star Trek sequel brings back stars Chris Pine (Capt. Kirk), Zachary Quinto (Spock), Anton Yelchin (Chekov) and Zoe Saldana (Uhura). It is produced by Abrams, Bryan Burk, Damon Lindelof, Alex Kurtzman and Roberto Orci.

Abrams' first Star Trek film, released in 2009, grossed $385 million worldwide.