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Diploma Thesis from the year 2002 in the subject Physics - Theoretical Physics, grade: 1,3 (A), University of Potsdam, language: English, abstract: This diploma thesis analyses static and spherically symmetric perfect fluid solutions to Einstein's field equations with cosmological constant. Constant density solutions are derived for different values of the cosmological constant. Eleven types of solutions are found, with an overview given at page 41. Furthermore the existence of a global solution is proved for a cosmological constant smaller than 4 Pi the boundary density, which is given by the equation of state.