To know whether there was a Black Taj Mahal, read this article about the legend of the Black Taj Mahal.
Black Taj Mahal Myth
According to the Black Taj myth, Shah Jahan had planned to build mirror image of the Taj Mahal he built for Mumtaz, albeit in black, on the other side of the river and connect the two by a bridge. This Black Taj was to be dedicated to Shah Jahan himself. A European traveler by the name of Jean Baptiste Tavernier who visited Agra in 1665 first mentioned the idea of Black Taj in his fanciful writings. And considering Shah Jahan's obsession with symmetry, the idea certainly seems plausible. More credibility to the story is added by an observation made by archeologists in 2006, when they reconstructed part of the pool in the moonlit garden and it reflected a dark reflection of the white mausoleum. The writings of Tavernier mention that Shah Jahan began to build his own tomb on the other side of the river but could not complete it as he was deposed by his own son Aurangzeb.
Fuel to the fire is further added as some scholar suggests that the blackened marbles in Mehtab Bagh that lie on the other side of the river are actually grim remains and foundations of an abandoned plan. On the other hand, other section of scholars totally dismiss the theory of Black Taj as it was discovered that the black marble remains in the Mehtab Bagh are not natural black but have become black over the course of time due to staining and wear and tear. Also, Mehtab Bagh was built by the first Mughal Emperor Babur, years before construction of Taj Mahal even started. The theory is once again dismissed by some scholars who believe that if Shah Jahan wanted to build a Black Taj Mahal, he would have started working on it immediately after completion of the first Taj Mahal in 1653, after which he had 5 years before he got arrested. While historians continue to argue over it, the idea of a Black Taj standing in front of the White Taj certainly keeps the anticipations and imaginations on a high.