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General Relativity and Gravitation

, Volume 32, Issue 7, pp 1365–1380 | Cite as

Differentially Rotating Disks of Dust

  • Marcus Ansorg
  • Reinhard Meinel
Article

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.

Rotating bodies disks of dust Ernst equation Jacobi's inversion problem Bäcklund transformations 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Marcus Ansorg
    • 1
  • Reinhard Meinel
    • 2
  1. 1.Fakultät für Mathematik und Informatik, GraduiertenkollegFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Theoretisch-Physikalisches InstitutFriedrich-Schiller-Universität JenaJenaGermany

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