Black brane solutions governed by fluxbrane polynomials

Abstract

A family of composite black brane solutions in the model with scalar fields and fields of forms is presented. 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 H_s (s = 1, ..., m) obeying non-linear differential equations with certain boundary conditions imposed. These master equations are equivalent to Toda-like equations and depend upon the non-degenerate (m x m) matrix A. It was conjectured earlier that the functions H_s should be polynomials if A is a Cartan matrix for some semisimple finite-dimensional Lie algebra (of rank m). It is shown that the solutions to master equations may be found by using so-called fluxbrane polynomials which can be calculated (in principle) for any semisimple finite-dimensional Lie algebra. Examples of dilatonic charged black hole (0-brane) solutions related to Lie algebras A_1, A_2, C_2 and G_2 are considered.

16 pages, Latex, no figures, several typos are corrected

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Cited by in corpus (11)

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• Higher-$n$ triangular dilatonic black holes
• Discreteness of dyonic dilaton black holes
• On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
• On generalized Melvin solution for the Lie algebra $E_6$
• On generalized Melvin solutions for Lie algebras of rank 3
• On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras
• Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras
• On generalized Melvin solutions for Lie algebras of rank 4
• Dilatonic dyon black hole solutions
• Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field