forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 2927
Articles: 2'007'093
Articles rated: 2575

22 October 2020
  » arxiv » gr-qc/0503043

 Article overview

Monodromy data parametrization of the spaces of local solutions of integrable reductions of Einstein's field equations
G. A. Alekseev ;
Date 9 Mar 2005
Journal Theor.Math.Phys. 143 (2005) 720-740; Teor.Mat.Fiz. 143 (2005) 278-304
Subject General Relativity and Quantum Cosmology; Exactly Solvable and Integrable Systems | gr-qc hep-th nlin.SI
AbstractFor the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein’s field equations are shown to be the subspaces of the spaces of local solutions of the ``null curvature’’ equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. The spaces of local solutions of these constraint ``null curvature’’ equations can be parametrized by a finite set of holomorphic functions of the spectral parameter which can be interpreted as a complete set of the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. The direct and inverse problems of such mapping (``monodromy transform’’), i.e. the problem of finding of the monodromy data for any local solution of the ``null curvature’’ equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problem are derived. The explicit forms of the monodromy data corresponding to the spaces of solutions of Einstein’s field equations are determined.
Source arXiv, gr-qc/0503043
Services Forum | Review | PDF | Favorites   
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
of broad interest:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser CCBot/2.0 (
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2020 - Scimetrica