Shahrbānū (or Shahr Banu) (Persian: شهربانو) (Meaning: "Lady of the Land"), is a personage described to have been one of the daughters of Yazdegerd III, the last Emperor of the Sassanid dynasty of Persia/Iran. Other names by which she has been referred to include: Shaharbānawayh, Shahzanān, Salāma, Salāfa, Ghazāla, Salama, and Sādira.
Shahrbānū was one of the wives of Husayn ibn Ali, (grandson of Muhammad and third Twelver Shī`a Imām) and the mother of Ali ibn Husayn (the fourth Twelver Shī`a Imām).
Western academic historians have cast doubt on the legend. A thorough treatment of the matter can be found in the Encyclopedia Iranica:

The account was subsequently greatly elaborated.
Having been brought to Madinah, `Ali allowed the ladies freedom in choosing whomever they wanted to marry from the Muslims, to which Shahrbānū was famously reported to have replied, "I want a head over whom there is no head".
Shahrbānū chose the hand of Husayn ibn `Ali in marriage and one of her sisters chose Muhammad ibn Abu Bakr. `Ali foretold the birth of the next Shī`a Imām as he said to Husayn: "Treat this lady kindly, for she will bear you the best of the people of the Earth after you. She is the mother of the trustees (of authority), the pure progeny".
According to Shī`a belief, Shahrbānū died shortly after giving birth to her son Ali ibn Husayn, and was thus not present at Karbalā. The eighth Twelver Shī`a Imām, Ali ar-Ridha has also been quoted as saying, "(Shahrbānū) died during her confinement, and one of (Husayn's) slave-wives looked after him (Ali ibn Husayn). The people claimed that (the slave-wife) was his mother, while she was his retainer".
The shrine of Shahrbānū can be found in ancient Rayy, in the southern suburbs of Tehran, Iran. ( )
According to legend, Shahrbānū was present at the bloody Battle of Karbalā. The legend tells that as the battle drew near, Husayn sat Shahrbānū on his famous white steed, Dhul Janāh, and bid her to return to her homeland in Persia. Husayn was quoted to have said, "You are a princess and not one of us, nor is this your war." Riding the light-footed steed, Shahrbānū was carried to the heart of Persia and the city of Rayy. There the enemy caught up with her, as she ran into a sheer cliff of a mountain. At this point, the legend maintained that the mountain cracked open and swallowed her and the steed up into itself - thus her shrine is found where it is today.
However it can be certain that this is only a legend as Husayn was riding on Dhul Janāh till the very last moments before his death in the Battle of Karbalā.
Even amongst the Iranian scholars there has been some dispute as to the existance of of a Persian princess by the title of Shahrbānū. The scholars Ali Shariati and Ayatullah Mutahhari are amongst those who have declared that any narrations pertaining to Shahrbānū are weak and false. Whereas Al-Mubarrad, al-Dinawari, Allameh Tabatabaei and many others disagree, and contend that Shahrbānū was the mother of Ali ibn Husayn, the fourth Twelver Shī`a Imām. Narrations of Shahrbānū have also been reported in Sunni sources including, "Bab 27" of Qabusnama, where Salmān the Persian is recounted to have been involved in the selection of Husayn by Shahrbānū.