Now, the chatter involves a different question: Why hasn’t he moved in?

The owner, Mukesh Ambani, and his spokesman have declined to discuss the matter, leaving the theorists plenty of room to ruminate. One popular explanation is that, despite the time and money lavished upon it, the building does not conform to the ancient Indian architectural doctrine known as Vastu Shastra. (More on that below.)

Certainly the home — which is called Antilia and according to Indian news reports has three helipads, six floors of parking and a series of floating gardens — looks lived in.

At night, the cantilevered tower is lit up bottom to top, inside and out. Members of the city’s moneyed class report attending movie screenings in the theater and eating dinners in the grand ballroom, served by a staff trained by the luxury Oberoi hotel chain.

Yet, friends of the family say that after the last canapés have been served and the guests bidden goodbye, the Ambanis often decamp to Sea Wind. That is the more modest, 14-story apartment tower at the south end of the city that Mr. Ambani, his wife, Nita, and three children, share — on different floors — with his mother and his estranged younger brother, Anil, and Anil’s family.

When does Mukesh Ambani plan to actually move into Antilia?

“I have asked him the question twice,” said a friend who has attended several parties there. He asked not to be identified for fear of ruining his relationship with Mr. Ambani, whose net worth Forbes has estimated at $27 billion. “He said, ‘Yes, we’ll go next month. Let it be done.’ They don’t talk about it.”

Another close family friend confirmed that the Ambani family did not live at Antilia but said they did sleep there “sometimes.” This friend, who also insisted on anonymity to avoid offending Mr. Ambani, had no explanation.

Tushar Pania, a spokesman for Mr. Ambani’s company, Reliance Industries, dismissed questions about whether the family was living at Antilia as idle gossip. “It’s a private home. There is no reason to discuss it in public.”

He said the family had moved in, but when asked whether the family still lived at Sea Wind, he revised: “They live in both places.”

But why would someone build what is widely considered the world’s most expensive private residence and then use it as a pied-à-terre?

Some friends, business associates and Ambani watchers posit the Vastu explanation, which gained wider currency earlier this year when DNA, an English-language newspaper in Mumbai, published an article about it citing “sources in the know.”

Vastu, a philosophy particularly significant in Hindu temple architecture, emphasizes the importance of directional alignments that create spiritual harmony. Many Hindus believe that living in a building not built according to vastu principles brings bad luck.

Basannt R. Rasiwasia, a Vastu expert whose clients include prominent businessmen and their families — although not Mr. Ambani — said Antilia appeared to run afoul of one of the key principles of Vastu: the building’s eastern side does not have enough windows or other openings to let residents receive ample morning light.

“From the outside what I see is that the eastern side is blocked while the western side is more open,” he said. “This always leads to misunderstanding between team members or sometime may create issues. This also indicates more hard work to achieve moderate success. There is more negative energy coming from the western side.”

Mr. Rasiwasia cautioned that he could not provide a full analysis since he had not been inside the building, which was designed by the architectural firm Perkins Will and the interior design firm Hirsch Bedner Associates, both American. Officials from the firms declined to comment, citing confidentiality agreements.

Even before it was built, Antilia was clouded by controversy. Mr. Ambani acquired the plot where the tower sits, on Altamount Road, in 2002. He bought it for 215 million rupees ($4.4 million) from a Muslim charitable trust that elsewhere operated an orphanage.

Muslim political leaders and other critics said the land was sold for only a small fraction of its market value. Mr. Ambani acquired the property in an auction, and his spokesman has denied allegations that he paid less than the land’s market value.

Last year, as Antilia was nearing completion, many Mumbai residents criticized the building as an ostentatious display of wealth in a country where most people live on less than $2 a day and a city where more than half the population lives in slums. Many domestic and foreign newspapers — including The New York Times — wrote about those sentiments, which one friend said upset the Ambanis.

Gyan Prakash, a history professor at Princeton University who wrote the book “Mumbai Fables,” said the criticism could have influenced the family’s decision not to make Antilia their full-time residence.

“It is one thing to brashly announce your arrival in the billionaire’s club by looking down on the rest of the city from your gated community in the sky,” he said via e-mail, “but then you may realize that it is lonely at the top!”

Even if the Ambanis now have reservations about Antilia, the building appears to have some admirers. A half-mile away, in the waterfront Breach Candy neighborhood that is home to the American consulate, another rich Mumbai business clan, the Singhania family, is building a tower with cantilevered floors. Many say it resembles Antilia.

The move-in date? Don’t ask.

Sagar Joshi, a spokesman for Raymond Ltd., the retail company controlled by the Singhanias, declined to answer questions about the building.

Neha Thirani contributed reporting.

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