Trudy Matematicheskogo Instituta imeni V.A. Steklova
General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Trudy Mat. Inst. Steklova:

Personal entry:
Save password
Forgotten password?

Trudy Mat. Inst. Steklova, 2016, Volume 295, Pages 7–33 (Mi tm3789)  

This article is cited in 2 scientific papers (total in 2 papers)

Integrable and non-integrable structures in Einstein–Maxwell equations with Abelian isometry group $\mathcal G_2$

G. A. Alekseev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We consider the classes of electrovacuum Einstein–Maxwell fields (with a cosmological constant) for which the metrics admit an Abelian two-dimensional isometry group $\mathcal G_2$ with nonnull orbits and electromagnetic fields possess the same symmetry. For the fields with such symmetries, we describe the structures of the so-called non-dynamical degrees of freedom, whose presence, just as the presence of a cosmological constant, changes (in a strikingly similar way) the vacuum and electrovacuum dynamical equations and destroys their well-known integrable structures. We find modifications of the known reduced forms of Einstein–Maxwell equations, namely, the Ernst equations and the self-dual Kinnersley equations, in which the presence of non-dynamical degrees of freedom is taken into account, and consider the following subclasses of fields with different non-dynamical degrees of freedom: (i) vacuum metrics with cosmological constant; (ii) space–time geometries in vacuum with isometry groups $\mathcal G_2$ that are not orthogonally transitive; and (iii) electrovacuum fields with more general structures of electromagnetic fields than in the known integrable cases. For each of these classes of fields, in the case when the two-dimensional metrics on the orbits of the isometry group $\mathcal G_2$ are diagonal, all field equations can be reduced to one nonlinear equation for one real function $\alpha(x^1,x^2)$ that characterizes the area element on these orbits. Simple examples of solutions for each of these classes are presented.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


Full text: PDF file (330 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 1–26

Bibliographic databases:

UDC: 517.958
Received: September 28, 2016

Citation: G. A. Alekseev, “Integrable and non-integrable structures in Einstein–Maxwell equations with Abelian isometry group $\mathcal G_2$”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 7–33; Proc. Steklov Inst. Math., 295 (2016), 1–26

Citation in format AMSBIB
\by G.~A.~Alekseev
\paper Integrable and non-integrable structures in Einstein--Maxwell equations with Abelian isometry group~$\mathcal G_2$
\inbook Modern problems of mechanics
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 295
\pages 7--33
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 295
\pages 1--26

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. G. Clement, D. Gal'tsov, “Stationary double black hole without naked ring singularity”, Class. Quantum Gravity, 35:21 (2018), 214002  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:170
    Full text:47
    First page:4

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022