Moulin Rouge!

In the year 1900, a depressed writer named Christian begins writing on his typewriter ("Nature Boy"). One year earlier, Christian moved to the Montmartre district of Paris to become a writer among members of the area's Bohemian movement. He encounters performers led by Toulouse-Lautrec; his writing skills allow them to finish their proposed show, "Spectacular Spectacular", that they wish to sell to Harold Zidler, owner of the Moulin Rouge. The group arrives at the Moulin Rouge as Zidler and his "Diamond Dog Dancers" perform for the audience ("Lady Marmalade/Zidler's Rap (Can Can)/Smells Like Teen Spirit"). Toulouse arranges for Christian to see Satine, the star courtesan, in her private quarters to present the work, unaware that Zidler is promising Satine to the wealthy and unscrupulous Duke of Monroth, a potential investor in the cabaret ("Sparkling Diamonds" medley).
Satine mistakes Christian for the Duke, and dances with him before retiring to her private chamber with him to discuss things privately ("Rhythm of the Night), but soon learns he is just a writer; by this time Christian has fallen in love with her ("Your Song"). The Duke interrupts them; Christian and Satine claim they were practicing lines for "Spectacular Spectacular". With Zidler's help, Toulouse and the rest of the troupe pitch the show to the Duke with an improvised plot about an evil maharajah attempting to woo an Indian courtesan who loves a poor sitar player ("The Pitch (Spectacular Spectacular)"). The Duke backs the show on the condition that only he may see Satine. Satine contemplates on Christian and her longing to leave the Moulin Rouge to become "a real actress" ("One Day I'll Fly Away"). Christian goes back to Satine to convince her that she loves him ("Elephant Love Medley"). As the cabaret is converted to a theater, Christian and Satine continue seeing each other under the pretense of rehearsing Satine's lines. The Duke becomes jealous and warns Zidler that he may stop financing the show; Zidler arranges for Satine to dine with the Duke that evening, but she falls ill from tuberculosis ("Górecki"). Zidler makes excuses to the Duke, claiming that Satine has gone to confession ("Like a Virgin"). Zidler learns that Satine does not have long to live. Satine tells Christian that their relationship endangers the show, but he counters by writing a secret love song to affirm their love ("Come What May").
As the Duke watches Christian rehearsing with Satine, Nini, a jealous performer, points out that the play is a metaphor for Christian, Satine and the Duke. Enraged, the Duke demands the ending be changed so that the courtesan ends up with the maharajah; Satine offers to spend the night with the Duke to keep the original ending. At the Duke's quarters, Satine sees Christian on the streets below, and realizes she cannot go through with this ("El Tango de Roxanne: "Roxanne/Tanguera"). The Duke tries to rape her, but she is saved by Le Chocolat, one of the cabaret dancers, and reunited with Christian, who urges her to run away with him. The Duke tells Zidler he will have Christian killed if Satine is not his. Zidler reiterates this warning to Satine, but when she refuses to return, he finally informs her she is dying ("A Fool to Believe"). Satine tells Christian they can no longer see each other as she will be staying with the Duke ("The Show Must Go On"). Christian tries following her, but is denied entry to the Moulin Rouge, and becomes depressed, even though Toulouse insists that Satine loves him.
The night of the show, Christian sneaks into the Moulin Rouge, intending to pay Satine to return his love just as the Duke paid for her ("Hindi Sad Diamonds"). He catches Satine before she steps on stage and demands she tell him she does not love him. Suddenly they find themselves in the spotlight; Zidler convinces the audience that Christian is the disguised sitar player. Christian denounces Satine and walks off the stage. From the rafters, Toulouse cries out, "The greatest thing you'll ever learn is just to love and be loved in return", spurring Satine to sing the song Christian wrote to express their love. Christian returns to the stage, joining her in the song. The Duke's bodyguard tries to kill Christian, but is thwarted, while the Duke's own attempt is stopped by Zidler. The Duke storms out of the cabaret as Christian and Satine complete their song ("Come What May (Reprise)", "Coup d'État (Finale)").
After the curtain closes, Satine succumbs to tuberculosis. She and Christian affirm their love before she dies. A year later the Moulin Rouge has closed down, and Christian is writing the tale of his love for Satine, a "love that will live forever" ("Nature Boy (Reprise)").

Question: Who does Satine think Christian actually is?
Answer: The Duke