Elliptic solutions of stationary axisymmetric Einstein equations

Abstract

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.