The Public Theater, New York Hathaway gives a heightened performance as a drone pilot and director Julie Taymor turns up all the dials, in a chilling play about the effects of killing by remote control

The nameless heroine of George Brant’s Grounded has a schedule many working mothers will recognise. She wakes up, takes her daughter to daycare, goes to her job, comes home, eats dinner with her husband, watches TV and falls asleep. Here’s the twist: the woman is a fighter pilot, and her job entails dropping missiles on military-age males, thousands of miles away. Every day, she sits in a chair at a Nevada airforce base and remotely controls a drone aircraft.

Brant’s monologue, which was seen in Edinburgh in 2013 and off-Broadway in 2014, is back, with a rather more famous figure filling out the flight suit: the Hollywood star Anne Hathaway, who pursued the role after reading a review of an earlier production. She approached Oskar Eustis, the artistic director of the Public theater, and he teamed her with Julie Taymor (of Lion King fame and Spider-Man infamy). This production, unnervingly gorgeous and overwrought, considers the costs of fighting a foreign war from home.

Facebook Twitter Pinterest ‘Taymor’s command of lighting, sound and projections is unparalleled’ … Grounded. Photograph: Joan Marcus

Hathaway’s pilot wasn’t always a virtual fighter; she flew through several tours in Iraq. She feels most alive, vibrant and whole when she’s up in “the blue”. But after she was grounded by her pregnancy, she went to work with the “chair force”: a group of pilots controlling drones from the safety of BarcaLoungers while staring at a screen at “a world carved out of putty”. So blue has turned to grey. Brant has a stable of metaphors – that blue and that grey, desert sand – and he rides them hard.

You notice these metaphors because Hathaway and Taymor take such pains to materialise and substantiate them, making the figurative literal at every opportunity. As usual, Taymor’s command of lighting, sound and projections is unparalleled. The stage is a raked sand floor, backed by a dark mirror. But on that sand, Taymor conjures up escalators, highways, the Vegas strip, and the statistics and shadows that the pilot sees on her screen. Taymor shows us the blue and the grey and all the shades in between.

Hathaway, too, is at pains to accentuate every syllable. She wouldn’t be the first actor you’d think to cast in such a macho role, and she knows it. This is a consciously chameleonesque performance: movie glamour is exchanged for scraped-back hair and minimal makeup; mid-Atlantic vowels for Wyoming drawl. In the opening moments, Hathaway shows just how hard she’s working to make this character persuasive. But eventually she relaxes into it. Or maybe we relax into her. The script demands a heightened performance, especially as the pilot grows increasingly unstrapped from observable reality, and Hathaway delivers. Monomania is one of her specialties, and she goes full throttle here.

Brant’s play is a small one. Even as the issues it approaches are vital, his theatrical interests are local rather than global, and rightly so. He’s more concerned with the psychological side-effects of remote warfare on this one woman than with a larger discussion of how it alters the military landscape or the world’s vision of the US. It’s up to us to do the extrapolating.

Or it should be. The breadth of the design and the intensity of the performance try to widen out the play in ways that don’t always flatter the script, flattening its ambiguities, underscoring and emphasising symbols and echoes that were already fairly obvious. And yet, the conclusion still chills. Drone aircraft, the play suggests, have removed the threat, for one side at least, of death from war. But at terrible, incalculable cost.

• At the Public theater, New York, until 24 May. Box office: 212-967 7555