The legend has it, that Shah Jehan decided to construct another Taj Mahal in black marble
on the other side of the river Yamuna and to connect the two by a bridge. This structure was
intended to be his own tomb. It has been recorded by Tavernier : "Shah Jehan began to build his own tomb on
the other side of the river but the war with his sons interrupted
his plan and Aurangzeb who reigns at present is not disposed to complete it". Later gazetteers and
guide books mention this story almost invariably. The irregular position of the cenotaph of Shah
Jehan as compared to that of Mumtaz Mahal which occupies the exact centre of the hall is enough proof into itself..
The Mehtab Burj and the wall adjoining it opposite the Taj Mahal are
generally said to be the grim remains of the proposed plan.

Shikha ji is atmost Right, But I read somwhere, After death of Mumtaj, Shajehan took decesion as given below ji

Rather it should hv been called red taj and should hv been built out of bones of slaves who died in constructing the taj mahal.

Shayad taj ke same ek aur banane ki koshish thee par jam nahi payi