We examine static perfect fluid spheres in the presence of a cosmological constant. Because of the cosmological constant, new classes of exact matter solutions are found. One class of solutions requires the Nariai metric in the vacuum region. Another class generalizes the Einstein static universe such that neither its energy density nor its pressure is constant throughout the spacetime. Using analytical techniques we derive conditions depending on the equation of state to locate the vanishing pressure surface. This surface can, in general, be located in regions where, going outwards, the area of the spheres associated with the group of spherical symmetry is decreasing. We use numerical methods to integrate the field equations for realistic equations of state and find consistent results.

• Received 12 November 2007

DOI:https://doi.org/10.1103/PhysRevD.77.064008