  A multidimensional model with (at most) one curved factor space and n
Ricci-flat internal spaces is considered, with arbitrary numbers of dilatonic
scalar fields and antisymmetric forms of both electric and magnetic types,
associated with p-branes in theories like M-theory. The problem setting covers,
in particular, homogeneous cosmologies, static, spherically symmetric and
Euclidean models. Exact solutions are obtained when the p-brane dimensions and
the dilatonic couplings obey orthogonality conditions in minisuperspace.
Conditions for black hole and wormhole existence among static models are
formulated. For black holes, a kind of no-hair theorem, leading to F-form
selection, is obtained; it is shown that even in spaces with multiple times a
black hole may only exist with its unique, one-dimensional time; infinite
Hawking temperature is explicitly shown to imply a curvature singularity at an
assumed horizon, and such cases among extreme black-hole solutions are
indicated.
