THE EINSTEINIAN GRAVITATIONAL-FIELD OF THE RIGIDLY ROTATING-DISK OF DUST

This paper presents the gravitational field of a uniformly rotating st ationary and axisymmetric disk consisting of dust particles as a rigor ous global solution to the Einstein equations. The problem is formulat ed as a boundary value problem of the Ernst equation and solved by mea ns of inverse methods. The solution is given in terms of linear integr al equations and depends on two parameters: the angular velocity OMEGA and the relative redshift z from the center of the disk. The Newtonia n limit z much less than 1 represents the MacLaurin solution of a rota ting fluid in the disk limit. For z --> infinity the '' exterior '' so lution is given by the extreme Kerr solution. This proves a conjecture of Bardeen & Wagoner (1969, 1971).