8 research outputs found
Harrison transformation of hyperelliptic solutions and charged dust disks
We use a Harrison transformation on solutions to the stationary axisymmetric
Einstein equations to generate solutions of the Einstein-Maxwell equations. The
case of hyperelliptic solutions to the Ernst equation is studied in detail.
Analytic expressions for the metric and the multipole moments are obtained. As
an example we consider the transformation of a family of counter-rotating dust
disks. The resulting solutions can be interpreted as disks with currents and
matter with a purely azimuthal pressure or as two streams of freely moving
charged particles. We discuss interesting limiting cases as the extreme limit
where the charge becomes identical to the mass, and the ultrarelativistic limit
where the central redshift diverges.Comment: 20 pages, 9 figure
Elliptic solutions of stationary axisymmetric Einstein equations
In this paper we present a more transparent version of an earlier construction of genus g algebraic-geometric solutions of the Einstein equation. For one of the metric coefficients we obtain a new expression that allows us to construct the coefficient in terms of derivatives of the function Psi ( lambda ) (solution of associative linear system). Finally, we proceed with an analysis of the two simplest genus 1 (elliptic) solutions
On the link between different U-V pairs and related finite-gap solutions of the stationary axisymmetric Einstein equation
An explicit link between finite-gap solutions of the stationary axisymmetric Einstein equation found by Korotkin and Matveev (1990) is obtained