Multidimensional gravity, flux and black brane solutions governed by polynomials

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 Hs (for fluxbranes) and Hs (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for Hs and Hs are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions Hs and Hs, 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 Hs were shown to be used for the construction of black brane polynomials Hs. This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A2, C2, and G2. © 2014 Pleiades Publishing, Ltd.