Differentially rotating disks of dust

Details Differentially rotating disks of dust Differentially rotating disks of dust

1999-10-13

arxiv.org/abs/gr-qc/9910045v2

Gen.Rel.Grav.32:1365-1380,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 3 figures. To appear in "General Relativity and Gravitation". Second version with minor corrections

Scientific paper

10.1023/A:1001950922865

We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer-Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Baecklund transformations to appropriate seed solutions of the Weyl class.

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