Indian actors Aishwarya Rai Bachchan, right, and Abhishek Bachchan have had a baby girl. (Joel Ryan/Associated Press)

One of Bollywood's most famous couples -- actress and model Aishwarya Rai Bachchan and her actor husband Abhishek Bachchan -- have had a baby girl. The infant, dubbed Baby B by the Indian press, was born Wednesday in Mumbai, with the excited father tweeting: "It's a girl."

Megastar Amitabh Bachchan, grandfather of the new arrival, announced his excitement in another tweet. "I AM DADA to the cutest baby girl, A dada ji ... Ecstatic," he wrote, using the Hindi word for paternal grandfather.

The baby, as yet unnamed, is the newest addition to one of Bollywood's most famous acting dynasties, one of a handful of families that dominate India's massive film industry. Her grandfather has had a 50-year career in movies, while her grandmother is actress Jaya Bhaduri Bachchan. Her parents -- a second-generation film star and a former Miss World -- were wed in 2007 in a private ceremony that drew a frenzy of media attention. There is little doubt among fans that the baby is destined for stardom.

Such is the power of the family that TV vans were kept at a distance from the hospital, where the Bachchans had three rooms. India's Broadcast Editors Association issued a 10-point advisory to its members on how to cover the birth, in an effort to curb obsessive speculation about the date of Baby B's arrival and the infant's gender. Grandpa Bachchan applauded the media's restraint on Twitter, after releasing the birth news.

Many are also curious to see whether the new mum continues her acting career. Marriage spells the end of film appearances for many Bollywood actresses, but she continued pursuing her career after her wedding. As a mother, she may have more difficulty getting glamorous roles. Still, if anyone can break the taboo, it's this Bollywood power couple.