Jake Gyllenhaal by Daniele Venturelli/ WireImage.com Jake Gyllenhaal by Daniele Venturelli/ WireImage.com
Jake Gyllenhaal's conspicuous absence from the news following

Heath Ledger's death has left many speculating about his response to the tragedy. As Ledger's

Brokeback Mountain costar and the godfather to the late actor's daughter, Gyllenhaal is considered to have been one of his closest friends. TMZ reports, however, that Jake is on location in New Mexico for a film shoot, but is deeply saddened and will not speak to the press. The set has been closed off to non-crew members and there are reports of beefed-up security to protect the actor's privacy. The production of his new film, Brothers, has reportedly continued, despite the extra measures to keep media out. - Anna Dimond Related: " Heath Ledger's Family: "Our Hearts Are Breaking," Plus, New Findings " News: Fox Newsman Apologizes After Controversy, More Updates " Video Blog: Ellen DeGeneres Pays Tribute to Heath Ledger " News: Olsen Twin Called Before 911; Plus, Jack Nicholson's Warning " News: Heath Ledger Autopsy "Inconclusive" " Watch video: News coverage of Ledger's shocking death " Watch video: Clips from Ledger's films " Photo gallery: Heath Ledger's life in pictures