A hyperelliptic solution class for the hyperbolic Ernst equation

2013/12/18 by Sebastian Moeckel, Moeckel, Sebastian
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1312.5356

14 pages, 2 figures

arxiv created 2013/12/18 · arxiv updated 2013/12/23

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.

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