English

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.

Keywords

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

R2 v1 2026-06-22T02:31:03.711Z