What is great acting? Hard to define, but you know it when you see it. And Robert Lindsay as Aristotle Socrates Onassis in a new play by Martin Sherman first seen in the Chichester Minerva Theatre, is the full mixed meat kebab: a performance of foul-mouthed arrogance, physical transformation, dominant authority and full-on vulgarian extravagance.

Sherman openly acknowledges plundering Peter Evans’ book Nemesis, in which it is suggested that Onassis conspired in, or even arranged, the assassination of Bobby Kennedy in 1968.

The play swallows this allegation and regurgitates it through the central love story of Onassis and Lydia Leonard’s square-jawed, fascinated Jackie Kennedy (he seduced the philandering JFK’s wife on his yacht while having an affair with her sister), leaving the spurned lover Maria Callas (Anna Francolini) to kvetch on the sidelines like an operatic Cassandra.

Using direct address, a chorus of old friends and colleagues on his Greek island - Katrina Lindsay’s classical white design has a river running through it, or at least along the front of the stage - and a sense of come-uppance for bad behaviour, Sherman and director Nancy Meckler concoct a modern Greek tragedy out of the legendary interaction between the self-made shipping magnate and the Washington political aristocracy.

There’s an insistent premonition of disaster in the fate of Onassis’ son (a striking Tom Austen) as the storm clouds gather and Lindsay collapses under the weight of his own guilt and inability to contemplate grief.

Lindsay paints a full portrait of aggressive sensuality and shocking self-centredness. Above all, he irradiates that physical stillness, charisma and banked down violence of all the big moguls and makes a good case for the old rogue being a top monster of the last century.

His choric entourage in the island taverna includes Gawn Grainger as a tongue-twisting guide to the incestuous celebrity labyrinth of the early 1960s, Liz Crowther and Sue Kelvin as baffled and comforting islanders, and John Hodgkinson as a notably tall suited side-kick turned bringer of bad news. It’s not a perfect play, but it’s a colourful cautionary tale for our celebrity times, with a knockout star turn at the centre.

- Michael Coveney

Martin Sherman has written several memorable plays but it strikes me that he’s got the timing of this one very wrong. Not only are most of the characters barely half-remembered but Onassis’s ruthless business methods seem particularly out of sync right now.

No doubt much of the attention will focus on Onassis’s startling claim that he was responsible for the assassination of Robert Kennedy, as made in a recent book. Needless to say, the play produces no evidence for such a claim beyond Onassis’s visceral hatred of Kennedy. But then, the play also suggests that Onassis and Jackie Kennedy were carrying on their affair while she was still married to JFK and that, in addition, she also had a sexual relationship with Bobby Kennedy after the president’s assassination. Sherman is obviously of the opinion that if a playwright speculates, he may as well do so wildly.

Sherman’s assertions wouldn’t be so bad if they were in a compelling play but far too much of Sherman’s writing is rather too obvious. You can almost imagine the thought processes at work: Onassis – Greek – Greek –chorus – mythology – bouzouki music; spice it up with a few half-baked conspiracy theories and stir it all together like a big bowl of avgolemono and serve.

But while the play itself failed to convince, the central performance of Robert Lindsay is utterly mesmerising. He captures the piratical nature of the businessman perfectly and one could glimpse the mixture of charisma and bullying that led to both his sexual and commercial success.

However, neither Elizabeth McGovern’s Jackie nor Diana Quick’s Maria could make us understand why they so bewitched him. McGovern’s husky tones sounded rather affected and I felt rather sorry for Quick trying to make sense out of Sherman’s rather overblown writing.

There should be a special mention for Julius D'Silva, who stepped into the role of Onassis’s confidante Costa at the last minute and who has to cope with a complicated speech about the relationships in the play – although it should be said that a play needing so much exposition is in trouble from the start.

Director Nancy Meckler tries to keep the play going without collapsing under its own verbiage – perhaps it would have been better if she’d trimmed the text a bit. This is a play memorable for Lindsay’s performance but little else.

- Maxwell Cooter