Sigma-model for Generalized Composite p-branes

A multidimensional gravitational model containing several dilatonic scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 ×M1 × . . . ×Mn, where Mi are Einstein spaces (i ≥ 1). The block-diagonal metric is chosen and all fields and scale factors of the metric are functions on M0. For the forms composite (electro-magnetic) p-brane ansatz is adopted. The model is reduced to gravitating self-interacting sigma-model with certain constraints. In pure electric and magnetic cases the number of these constraints is n1(n1 − 1)/2 where n1 is number of 1-dimensional manifolds among Mi. In the ”electro-magnetic” case for dimM0 = 1, 3 additional n1 constraints appear. A family of ”MajumdarPapapetrou type” solutions governed by a set of harmonic functions is obtained, when all factor-spaces Mν are Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M0 when also some additional ”internal” Einstein spaces of non-zero curvature are added to M . As an example exact solutions for D = 11 supergravity and related 12-dimensional theory are presented. PACS number(s): 04.50.+h, 98.80.Hw, 04.60.Kz