Black hole p-brane solutions for general intersection rules
Abstract
Black hole generalized p-brane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold that contains a product of n - 1 Ricci-flat ``internal'' spaces. They are defined up to a set of functions Hs obeying a non-linear differential equations (equivalent to Toda-type equations) with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions Hs for intersections related to semisimple Lie algebras is suggested. This conjecture is proved for Lie algebras: Am, Cm+1, m = 1,2,... Explicit formulas for A2-solution are obtained. Two examples of A2-dyon solutions (e.g. dyon in D = 11 supergravity and Kaluza-Klein dyon) are considered. Post-Newtonian parameters "beta" and "gamma" corresponding to 4-dimensional section of the metric are calculated. It is shown that "beta" does not depend upon intersections of p-branes. Extremal black hole configurations are also considered.
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