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Journal Article

Differentially Rotating Disks of Dust

MPS-Authors

Ansorg,  Marcus
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1365-1380.pdf
(Publisher version), 580KB

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Citation

Ansorg, M., & Meinel, R. (2000). Differentially Rotating Disks of Dust. General Relativity and Gravitation, 32(7), 1365-1380. doi:10.1023/A:1001950922865.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5711-C
Abstract
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 Bäcklund transformations to appropriate seed solutions of the Weyl class.