Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-06-13
Gen.Rel.Grav. 33 (2001) 309-338
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, 3 figures, submitted to 'General Relativity and Gravitation'
Scientific paper
In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.
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