A ug 1 99 8 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 = M 0 × M 1 ×. .. × M n , where M i are Einstein spaces (i ≥ 1). The block-diagonal metric is chosen and all fields and scale factors of the metric are functions on M 0. For the forms composite (electromagnetic) 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 n 1 (n 1 − 1)/2 where n 1 is number of 1-dimensional manifolds among M i. In the " electromagnetic " case for dimM 0 = 1, 3 additional n 1 constraints appear. A family of " Majumdar-Papapetrou type " solutions governed by a set of harmonic functions is obtained, when all factor-spaces M ν are Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M 0 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.