On multidimensional analogs of Melvin's solution for classical series of Lie algebras

Abstract

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra $\mathcal{G}$ is presented. The gravitational model contains n 2-forms and $l\ge n$ scalar fields, wheren is the rank of $\mathcal{G}$. The solution is governed by a set of n functions obeying n ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating of these polynomials for classical series of Lie algebras is suggested (see Appendix). The polynomials corresponding to the Lie algebra D_4 are obtained. It is conjectured that the polynomials for A_n-, B_n- and C_n-series may be obtained from polynomials for D_{n+1}-series by using certain reduction formulas.

6 pages, based on a report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow)

Cited by in corpus (5)

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• On generalized Melvin solution for the Lie algebra $E_6$
• On multidimensional cosmological solutions with scalar fields and 2-forms corresponding to rank-3 Lie algebras: acceleration and small variation of G
• Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras
• Properties of the magnetic universe with positive cosmological constant