NEW YORK—Rosamund Pike had been a Bond girl and a Greek goddess, but she had never acted opposite Tom Cruise’s bare chest before. In the crime thriller Jack Reacher, Pike plays a lawyer named Helen and Cruise plays an ex–military cop vigilante drifter named, well, Jack Reacher. At one point, Helen finds the proximity of Reacher’s decidedly buff, shirtless torso so distracting that there is only one thing to do. “Could you please put a shirt on,” Helen says, rather breathlessly.

Discussing the movie at a New York hotel, Pike—who looks exactly as blond, blue-eyed, and pretty as she appears on-screen—doesn’t particularly express how the chiselled Cruise physique affected her. “You know, Tom and I had a very easy chemistry,” says the British actor, who is skilled at being not British when needed. (She plays a perfectly believable Pittsburgher in this movie, for instance. In Die Another Day, Atonement, and Wrath of the Titans, she sounds as English as, well, herself.) “It was nothing we had to work on.”

Jack Reacher (which opens Friday [December 21]) is based on Brit author Lee Child’s novel One Shot, one of 17 in the popular Reacher series. The character roams America, righting wrongs and kicking wrongdoers’ asses. He has no credit cards and no such thing as a driver’s licence. In the movie, he “borrows” people’s car keys—including Helen’s—often wrecking their cars in high-speed chases. He has only one set of clothes, hence the need to rinse a bloodied shirt in a motel sink and, minus the shirt, discuss a sniper case with a blond lady lawyer.

“Reacher’s the guy who walks into town and he does things differently from everybody else,” Pike says. “Any sort of normal social interaction, he just kind of doesn’t behave properly and Helen is left sort of startled at every turn.” Helen “hasn’t got the brilliance of Reacher, and that drives her mad. It’s like she’s a girl who’s good at math and then she meets a mathematician.”

Pike doesn’t seem bothered that despite Reacher’s, er, physicality and Helen’s wide-eyed reactions, the relationship remains curiously chaste. (Reacher is introduced in the movie watching from a motel bed as a prostitute, presumably, delicately adjusts her thong underwear and hooks her bra.) “You know, Chris [writer-director McQuarrie] is such a good writer, he manages to give you all the satisfaction of a love affair without them ever having touched,” she says, then adds: “In a way, I started to think maybe sex scenes are what people put in when there isn’t any chemistry.”

David Oyelowo (pronounced “oh yellow oh”) had no such sexual-chemistry responsibilities. Playing a cop who’s also on the sniper case that begins to look like something deeper than an unhinged Iraq war veteran, the also-British actor concentrated on not being a cliché with a badge.

“Weird meeting you,” says Oyelowo’s Det. Emerson, understandably, after Reacher appears at the police station, demands to see the sniper-case evidence, then just as abruptly leaves.

“There was a world in which this could go on to be Lethal Weapon,” Oyelowo says, seated alongside Pike. “This could go on to be these two teaming up and going after the bad guys.” Instead, Emerson and Reacher have a decidedly antagonistic relationship, which Oyelowo considered “a lot of fun.…I have an allergic reaction to playing, especially as a black actor, the mandatory best-friend cop-detective type. You will never see me in that movie.”

Oyelowo (who’s appeared in The Help and Lincoln) was almost not in this movie. For plot reasons best left undiscussed, other Emersons were considered. In the end, the physically fit movie star was the decider. “It was Tom Cruise who just said, ‘He’s really good! Just put him in the role. What are you doing?’ ” McQuarrie says, seated near his movie detective.

Well, perhaps that wasn’t the entire story. “But also, what Chris is leaving out is the way he told me I got the role,” Oyelowo says. “He said, ‘Oh, I’ve just shown your tape to Tom Cruise and Tom said, “Can we get this guy?” ’ I thought, ‘ “Yes” would be the answer to that question.’ ”