Mathematics – Mathematical Physics
Scientific paper
Jun 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cmaph..39..131c&link_type=abstract
Communications in Mathematical Physics, Volume 39, Issue 2, pp.131-151
Mathematics
Mathematical Physics
67
Scientific paper
A detailed investigation is made of the simplest type of general relativistic perfect fluid cosmological models that possess a singularity at which all physical quantities are well-behaved. These models are spatially homogeneous, axisymmetric generalisations of the open ( k/it=-1) Robertson-Walker universes. A pictorial description of the evolution of the models is obtained by using the qualitative theory of differential equations. The most surprising feature that emerges is that for some (non-empty) models the matter density may become zero, within a finite time, on a null hypersurface which acts as a Cauchy horizon for the models. This result is generalized to most other types of spatially homogeneous models. It is also discovered that the behaviour of the models varies dramatically with the type of matter content. This casts some doubts on the validity of assuming definite equations of state in general relativity, and suggests an investigation of the structural stability of Einstein's field equations.
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