Differentially rotating disks of dust

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 Baecklund transformations to appropriate seed solutions of the Weyl class.

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

References in corpus (2)

• General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
• Solutions of Einstein's field equations related to Jacobi's inversion problem

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