The Einsteinian Gravitational Field of the Rigidly Rotating Disk of Dust
Abstract
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).
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1993
 DOI:
 10.1086/187005
 Bibcode:
 1993ApJ...414L..97N
 Keywords:

 Computational Astrophysics;
 Cosmic Dust;
 Cosmology;
 Einstein Equations;
 Gravitational Fields;
 Rotating Disks;
 Angular Velocity;
 Boundary Value Problems;
 Integral Equations;
 Quasars;
 Red Shift;
 Astrophysics;
 BLACK HOLE PHYSICS;
 GALAXIES: GENERAL;
 GRAVITATION;
 GALAXIES: QUASARS: GENERAL;
 RELATIVITY