A hyperelliptic solution class for the hyperbolic Ernst equation
Mathematical Physics
2013-12-23 v1 General Relativity and Quantum Cosmology
math.MP
Abstract
A new hyperelliptic solution class for the hyperbolic Ernst equation is obtained by transforming the regarding solution of the elliptic Ernst equation. Furthermore, a nontrivial way for obtaining general polarized colliding wave solutions from this hyperelliptic family of solutions is presented. The explicit form of the solutions for a Riemann surface of genus n=1 is given. In addition, an explicit example in terms of a Khan-Penrose seed is provided, emphasizing the importance of the presented procedure for generating general polarized colliding plane-wave space times from space-times with a collinear polarization of the colliding waves.
Cite
@article{arxiv.1312.5356,
title = {A hyperelliptic solution class for the hyperbolic Ernst equation},
author = {Sebastian Moeckel},
journal= {arXiv preprint arXiv:1312.5356},
year = {2013}
}
Comments
14 pages, 2 figures