General Relativistic Static Fluid Solutions with Cosmological Constant

Diploma Thesis from the year 2002 in the subject Physics - Theoretical Physics, grade: 1,3 (A), University of Potsdam, language: English, abstract: Dive into the esoteric realm where Einsteins theory of general relativity intertwines with the enigmatic cosmological constant, shaping the very fabric of stellar structures. This exploration unveils novel, static, and spherically symmetric solutions to the Einstein field equations, venturing beyond conventional astrophysical models. Journey through diverse solutions, from those where matter extends infinitely, painting a cosmos teeming with unseen connections, to those elegantly confined within finite boundaries, mimicking the familiar elegance of stars. Uncover the profound influence of the cosmological constant - a force both repulsive and alluring - on these cosmic entities. Witness how it warps the spatial geometry, dictating the curvature around massive bodies and influencing their ultimate fate. Delve into the heart of stellar modelling as the study meticulously dissects constant density configurations, navigating hyperbolic, Euclidean, and spherical geometries, each whispering tales of alternative universes. Further explore solutions with prescribed equations of state, leading to a deeper understanding of the relationship between pressure, density, and the elusive cosmological constant. Confront the limits of stellar existence through the derivation of a generalized Buchdahl inequality, rewritten for the era of cosmological precision. This inequality sets a fundamental bound on the mass of stellar objects. Discover how the interplay of these parameters dictates the existence and uniqueness of solutions, probing the very boundaries of physical possibility. Confront the challenge of singularities and explore the conditions under which they can be avoided, offering insights into the nature of spacetime itself. Finally, ponder the implications of finite radii solutions, bridging the gap between theoretical construct