It’s part satire, part social comment, all fragmented and downright inconclusive. But the biggest hint as to what Brady Corbet’s second feature actually is comes right at the end, as the credits scroll fashionably downwards instead of up. It’s “a 21st-century portrait”, we’re told. This might have been more useful at the beginning, but that’s not this director’s style. As he proved with his debut, the Michael Haneke-esque period drama The Childhood of a Leader – a study of the roots of fascism that seemed baffling when it debuted in Venice two years ago and made more sense three months later with the rise of Donald Trump – Corbet prefers to play the long game, and favours opening a conversation over narrative closure.

Corbet has always been an old head on young shoulders, and it should come as no surprise that his film about the pop world shows the spirit of the Danish provocateur Lars von Trier, for whom Corbet acted in 2011’s Melancholia. Split into chapters, with a dry narration from Willem Dafoe – another Von Trier favourite – Vox Lux charts a journey through recent history, starting in 1999 and ending in 2017. The start date proves immediately significant: in a veiled recreation of the Columbine school massacre, a troubled boy appears at a music lesson, killing the teacher instantly and spraying bullets at the teenage pupils. One girl, Celeste (Raffey Cassidy), refuses to be cowed and tries to talk the shooter down. For a second they seem to connect, then more shots are fired, catching Celeste in the neck and leaving a scar that will never heal.

The incident has unexpected repercussions. Recuperating in hospital, Celeste practises her music, tapping away on a keyboard with her sister Eleanor (Nymphomaniac’s Stacy Martin), who feels she somehow let Celeste down by not being in school that day. At a vigil for the victims, Celeste is unable to speak and instead offers a raw, plaintive, self-penned song. It immediately captures the nation’s mood (becoming, as The Narrator notes with amused disgust, “a hit”) and Celeste is thrown into show business at the age of 14.

Guided by her manager (Jude Law), a scruffy, even seedy-looking character who nevertheless always seems to have has her best interests at heart, Celeste takes the first steps into becoming a teen idol, dabbling with drugs and having a seemingly innocuous affair with a grungey rock star that will turn out to have consequences in the second half. So far, it’s been a freewheeling affair; Celeste and Eleanor’s first trip to Europe is a whirling, speeded-up Super 8 montage (a device Corbet uses throughout, to increasingly darker effect), and the girls are the best of friends. That is, until 2001, when a seismic shift in their private lives is echoed in the unseen aftermath of 9/11, where this particular chapter ends.

You might be wondering where the much-vaunted Natalie Portman figures in all this, and at around the midway point Lux Vox dramatically changes tone. It’s now 14 years later and Celeste is an adult with a teenage daughter (also played by Raffey Cassidy) from that casual fling. The transition is jarring; the meek, curious Celeste is long gone; in her place is a jaded thirtysomething diva, trying to hold on to her pop stardom after a scandal that her manager paid, apparently unsuccessfully, to go away. The colour palette is more aggressive now, and Celeste seems almost entirely transformed – a mash-up of chameleonic Lady Gaga, streetwise Madonna and autotuned Katy Perry – her hair hacked into a rock-chick quiff that will become more sculpted and artificial as the film unfolds.

This Celeste is a woman on the verge of yet another nervous breakdown, and there are hints, possibly unintended, of John Cassavetes’s Opening Night as she embarks on a series of comeback shows, starting in her hometown. Wavering between imperious arrogance and pathetic petulance, Celeste’s faltering confidence is further undermined when a terrorist cell in Europe starts to use part of her trademark iconography – a bejewelled mask – in their operations.

It all suggests that something major is coming, a finale that will finally bring these elements together with a payoff amounting to a sizeable scene or revelation. But Vox Lux is not about to resolve anything. Instead, it seems to be a series of equations, dealing most distinctly with the notion of fame in the modern world. It’s a film that asks, what is fame: promotion, manipulation or hero-worship? Can it really just be the end result of massive popularity? And how do we separate it from notoriety? It’s a good question to ask, even though, as the film readily shows, we’re far from getting the answer.