Dresden 2000 – scientific programme
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GR: Gravitation und Relativitätstheorie
GR 1: Klassische Allgemeine Relativit
ätstheorie
GR 1.4: Talk
Monday, March 20, 2000, 15:15–15:35, W B321
Differentiell rotierende Scheiben — •Marcus Ansorg1 and Reinhard Meinel2 — 1Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, Graduiertenkolleg, Ernst-Abbe-Platz 4, 07743 Jena, Germany — 2Friedrich-Schiller-Universität Jena, Theoretisch-Physikalisches Institut, Max-Wien-Platz 1, 07743 Jena, Germany
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. Reference: gr-qc/9910045