But Bernstein's children said their father, who wrote the music for West Side Story, had a "nice, big nose", and they feared attempts were being made to bring Cooper "down a notch".

In Maestro, the actor stars opposite Carey Mulligan in a drama that focuses on Bernstein's relationship with his wife, Felicia Montealegre.

In an official trailer released by Netflix, Cooper - known for A Star Is Born and American Sniper - is seen with a notably larger nose than his real one.

Some online commentators have posted pictures of Cooper and Bernstein side by side, pointing out that Cooper's prosthetic appears to be bigger than Bernstein's actual nose.

The conductor, who won 16 Grammy Awards, died in 1990.

Tracy-Ann Oberman, known for her roles in EastEnders and After Life, implied that Cooper should not have needed to wear a prosthetic.

She wrote on Instagram that if Cooper was chosen over a "Jewish A-lister who can equally play that role" then his acting should be "so magnificent and truthful that the character of Bernstein shines through what he already looks like".

She added: "If he needs to wear a prosthetic nose then that is, to me and many others, the equivalent of black-face or yellow-face.

"If Bradley Cooper can't do it through the power of acting alone then don't cast him - get a Jewish actor."

Bernstein's three children, however, said it "breaks our hearts to see any misrepresentations or misunderstandings" of Cooper's work.

They added: "It happens to be true that Leonard Bernstein had a nice, big nose.

"Bradley chose to use makeup to amplify his resemblance, and we're perfectly fine with that.

"We're also certain that our dad would have been fine with it as well."

Click to subscribe to Backstage wherever you get your podcasts

Jamie, Alexander and Nina Bernstein said they felt that "any strident complaints around this issue strike us above all as disingenuous attempts to bring a successful person down a notch - a practice we observed all too often perpetrated on our own father".

They said that Cooper "included the three of us along every step of his amazing journey as he made his film about our father".

They said they "could feel the profound respect and, yes, the love that Bradley brought to his portrait of Leonard Bernstein and his wife, our mother Felicia".

Read more:
Hollywood couple invite people to stay with them
How Oppenheimer's legacy still impacts today
Game of Thrones and EastEnders actor dies aged 36

They added: "We feel so fortunate to have had this experience with Bradley, and we can't wait for the world to see his creation."

Cooper also directed the movie, which is out in November, and co-wrote the screenplay.

Oberman is not alone in criticising the casting of Cooper. Daniel Fienberg, chief television critic with The Hollywood Reporter, tweeted earlier this year that it was "problematic".

There have also been objections to Cillian Murphy, who is not Jewish, playing the Jewish nuclear physicist Robert Oppenheimer.

David Baddiel has described such casting as "complacent" and linked to "Jewish erasure".

However, journalist and tech entrepreneur Brian Krassenstein said he was fine with Cooper playing Bernstein.

He posted on X, formerly known as Twitter: "Relax! Movies are art. An actor's job is to portray the character they play to the best of their ability.

"I'm Jewish. My nose is large. Many Jewish people's noses are large. It's just a fact."