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Multidimensional gravity, flux and black brane solutions governed by polynomials

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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.

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Authors and Affiliations

  1. Center for Gravitation and Fundamental Metrology, VNIIMS, Ozernaya ul. 46, Moscow, 119361, Russia

    V. D. Ivashchuk & V. N. Melnikov

  2. Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    V. D. Ivashchuk & V. N. Melnikov

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  1. V. D. Ivashchuk
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Correspondence to V. D. Ivashchuk.

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Based on a plenary talk given at the 11th International Conference on Gravitation, Astrophysica and Cosmology of Asia-Pacific Countries (ICGAC-11), October 1–5, 2013, Almaty, Kazakhstan.

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Ivashchuk, V.D., Melnikov, V.N. Multidimensional gravity, flux and black brane solutions governed by polynomials. Gravit. Cosmol. 20, 182–189 (2014). https://doi.org/10.1134/S0202289314030086

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