The Oppenheimer-Snyder space-time with a cosmological constant

We investigate the Oppenheimer-Snyder space-time with a positive cosmological constant A. The interior of the dust sphere is described by the closed Friedmann-Robertson-Walker space-time while the exterior is the Schwarzschild-de Sitter space-time. Due to the cosmological constant A, when the gravitational massM_o of the dust sphere is very large, there is no collapsing solution with the de Sitter-like asymptotic region which expands exponentially in the expanding universe frame. This fact suggests that the very large initial inhomogeneity does not necessarily lead to the failure of the cosmic no hair conjecture.