Mathematical Research Letters

Volume 9, Issue 1, January 2002 pp. 27-45.

Ernst equation, Fay identities and variational formulas on hyperelliptic curves

Authors: C. Klein, D. Korotkin, and V. Shramchenko
Author institution: Max-Planck-Institut für Physik, and Concordia University

Summary: We present a unified approach to theta-functional solutions of the stationary axisymmetric Einstein equations in vacuum. Using Fay's trisecant identity and variational formulas on hyperelliptic Riemann surfaces, we establish formulas for the metric functions, the Ernst potential and their derivatives.

Contents Full-Text PDF