Integrable spherically symmetric \(p\)-brane models associated with Lie algebras (Q1580914)

The authors consider a classical model of gravity theory involving several dilatonic scalar fields, where differential forms are interpreted as representing intersecting \(p\)-branes, in a pseudo-Riemannian product manifold \(M\) of dimension \(D\). It is shown that the equations of motion of the model can be reduced to the Euler-Lagrange equations for a pseudo-Euclidean Toda-like system. Assuming that the characteristic vectors of the configuration of \(p\)-branes are coupled to the dilatonic scalar fields, then these vectors may be interpreted as the root vectors of a Lie algebra of the types \(A_r\), \(B_r\), \(C_r\). In this case, the resulting model is reducible to one of the open Toda chains, and is completely integrable. The general solutions are exhibited, and a particular solution describing a class of nonextremal black holes is discussed. Contents include: an introduction (containing a brief survey of the topic); the general model; integration of the \(p\)-brane model with linearly independent characteristic vectors; general solutions for models associated with Lie algebras; the particular solution describing black holes; and a 30 item bibliography.