  We study the conditions under which a generic supergravity model involving
chiral and vector multiplets can admit viable metastable vacua with
spontaneously broken supersymmetry and realistic cosmological constant. To do
so, we impose that on the vacuum the scalar potential and all its first
derivatives vanish, and derive a necessary condition for the matrix of its
second derivatives to be positive definite. We study then the constraints set
by the combination of the flatness condition needed for the tuning of the
cosmological constant and the stability condition that is necessary to avoid
unstable modes. We find that the existence of such a viable vacuum implies a
condition involving the curvature tensor for the scalar geometry and the charge
and mass matrices for the vector fields. Moreover, for given curvature, charges
and masses satisfying this constraint, the vector of F and D auxiliary fields
defining the Goldstino direction is constrained to lie within a certain domain.
The effect of vector multiplets relative to chiral multiplets is maximal when
the masses of the vector fields are comparable to the gravitino mass. When the
masses are instead much larger or much smaller than the gravitino mass, the
effect becomes small and translates into a correction to the effective
curvature. We finally apply our results to some simple classes of examples, to
illustrate their relevance.
