  We discuss the linearization of Einstein equations in the presence of a
cosmological constant, by expanding the solution for the metric around a flat
Minkowski space-time. We demonstrate that one can find consistent solutions to
the linearized set of equations for the metric perturbations, in the Lorentz
gauge, which are not spherically symmetric, but they rather exhibit a
cylindrical symmetry. We find that the components of the gravitational field
satisfying the appropriate Poisson equations have the property of ensuring that
a scalar potential can be constructed, in which both contributions, from
ordinary matter and $\Lambda > 0$, are attractive. In addition, there is a
novel tensor potential, induced by the pressure density, in which the effect of
the cosmological constant is repulsive. We also linearize the Schwarzschild-de
Sitter exact solution of Einstein's equations (due to a generalization of
Birkhoff's theorem) in the domain between the two horizons. We manage to
transform it first to a gauge in which the 3-space metric is conformally flat
and, then, make an additional coordinate transformation leading to the Lorentz
gauge conditions. We compare our non-spherically symmetric solution with the
linearized Schwarzschild-de Sitter metric, when the latter is transformed to
the Lorentz gauge, and we find agreement. The resulting metric, however, does
not acquire a proper Newtonian form in terms of the unique scalar potential
that solves the corresponding Poisson equation. Nevertheless, our solution is
stable, in the sense that the physical energy density is positive.
