The Einsteinian gravitational field of the rigidly rotating disk of dust

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 and the relative redshift from the center of the disk. The Newtonian limit z is much less than 1 represents the MacLaurin solution of a rotating fluid in the disk limit. For z approaches infinity the 'exterior' solution is given by the extreme Kerr solution. This proves a conjecture of Bardeen and Wagoner (1969, 1971).