The consistent newtonian limit of Einstein's gravity with a cosmological constant

We derive the "exact" Newtonian limit of general relativity with a positive cosmological constant A. We point out that in contrast to the case with A = 0, the presence of a positive A in Einsteins's equations enforces, via the condition \ Phi \ much less than 1 on the potential Phi, a range R-max(Lambda) much greater than r much greater than R-min(Lambda), within which the Newtonian limit is valid. It also leads to the existence of a maximum mass, M-max(Lambda). As a consequence we cannot put the boundary condition for the solution of the Poisson equation at infinity. A boundary condition suitably chosen now at a finite range will then get reflected in the solution of Phi provided the mass distribution is not spherically symmetric.