## General Relativistic Static Fluid Solutions with Cosmological ConstantDiploma Thesis from the year 2002 in the subject Physics - Theoretical Physics, grade: 1,3 (A), University of Potsdam, 28 entries in the bibliography, 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. |

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### Contents

7 | |

3Solutionswith constantdensity | 15 |

4Solutionswith givenequation of state | 42 |

Appendices | 57 |

References | 65 |

Erklarung | 71 |

### Common terms and phrases

0.8 1 Pressure 1and afunctionof central pressure alpha anti-de Sitter solution boundary density Buchdahl variables central pressure 0.05 central pressure Pc const constant density solutions constant of integration constantdensity coordinate singularity corresponds cosh cosmological constants satisfying Cosmological eventhorizons cosmological term cosmologicalconstant deﬁned derived differential equation ea(r Einstein static universe Einstein tensor equations with cosmological exterior solution f¨ur ﬁeld finite ﬂuid Fluid Solutions Gauss coordinates geometry given gives group orbits held equations horizon implies Integration of 3.1 L¨osung L¨osungen metric model with exterior Newtonian limit object‘s radius Figure perfect fluid Pressure Figure pressure is decreasing pressure vanishes R(Pc radial coordinate regular centre Ricci tensor Riemann tensor Schwarzschild-de Sitter solution Schwarzschild-deSitter second centre sin2 solution is joined Solutions with Cosmological spatial spherically symmetric spherically symmetric spacetime stellar model stellar objects thecosmological thedensity theorem theradius tonian TOV-A equation upper bound vacuum solution volume of group Weyl tensor