This paper presents the gravitational field of a uniformly rotating stationary and axisymmetric disk consisting of dust particles as a rigorous global solution to the Einstein equations. The problem is formulated as a boundary value problem of the Ernst equation and solved by means of inverse methods. The solution is given in terms of linear integral equations and depends on two parameters: the angular velocity OMEGA and the relative redshift z from the center of the disk. The Newtonian limit z much less than 1 represents the MacLaurin solution of a rotating fluid in the disk limit. For z --> infinity the '' exterior '' solution is given by the extreme Kerr solution. This proves a conjecture of Bardeen & Wagoner (1969, 1971).
