2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99701Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.19 pages, 5 figures, 1 table, revised bibliography, corrected eqn. (3.11), typos corrected, two new referencesGeneral Relativity and Quantum Cosmologytext