Majumdar-Papapetrou Type Solutions in Sigma-model and Intersecting p-branes

TL;DR

This paper generalizes Majumdar-Papapetrou solutions within sigma-models, explores their relation to p-branes, and investigates special algebraic classes, providing new solutions and criteria for horizons and singularities.

Contribution

It introduces a block-orthogonal generalization of solutions, analyzes solutions linked to Lie and Kac-Moody algebras, and extends intersection rules in supergravity contexts.

Findings

Solutions depend on scalar product matrices of vectors U^s.

Orthogonal U^s lead to known solutions; non-orthogonal cases are new.

Criteria for horizons and singularities in multicenter solutions are established.

Abstract

The block-orthogonal generalization of the Majumdar-Papapetrou type solutions for the sigma-model studied earlier are obtained and corresponding solutions with p-branes are considered. The existence of solutions and the number of independent harmonic functions is defined by the matrix of scalar products of vectors $U^s$, governing the sigma-model target space metric. For orthogonal $U^s$, when target space is a symmetric homogeneous space, the solutions reduce to the previous ones. Two special classes of solutions with $U^s$ related to finite dimensional Lie algebras and hyperbolic (Kac-Moody) algebras are singled out and investigated. The affine Cartan matrices do not arise in the scheme under consideration. Some examples of obtained solutions and intersection rules for D=11 supergravity, related D=12 theory and extending them $B_D$-models are considered. For special multicenter solutions criterions for the existence of horizon and curvature singularity are found.