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Gravitation and Cosmology

, Volume 20, Issue 3, pp 182–189 | Cite as

Multidimensional gravity, flux and black brane solutions governed by polynomials

  • V. D. IvashchukEmail author
  • V. N. Melnikov
Article

Abstract

Two families of composite black brane solutions are overviewed, fluxbrane and black brane ones, in a model with scalar fields and fields of forms. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions \(\mathcal{H}_s \) (for fluxbranes) and H s (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for \(\mathcal{H}_s \) and H s are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions H s and \(\mathcal{H}_s \), as was conjectured and confirmed (at least partly) earlier, should be polynomials in proper variables if A is a Cartan matrix of some semisimple finite-dimensional Lie algebra. The fluxbrane polynomials \(\mathcal{H}_s \) were shown to be used for the construction of black brane polynomials H s . This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A 2, C 2, and G 2.

Keywords

Black Hole Solution Modulus Function Black Brane Cartan Matrix Brane Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Center for Gravitation and Fundamental MetrologyVNIIMSMoscowRussia
  2. 2.Institute of Gravitation and CosmologyPeoples’ Friendship University of RussiaMoscowRussia

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