TL;DR
This paper provides an overview of cosmological singularity theorems, including the necessary mathematical background and discussions on the scope of general relativity in cosmology.
Contribution
It offers a comprehensive introduction suitable for graduate students, detailing the mathematical framework and validity issues of singularity theorems in cosmology.
Findings
Summarizes key singularity theorems in cosmology
Discusses the mathematical tools from tensor and causal geometry
Addresses the limitations of general relativity in cosmological models
Abstract
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the mathematical notion of a cosmology is described in some detail and issues related to the range of validity of general relativity are also discussed.
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Taxonomy
TopicsRelativity and Gravitational Theory · Advanced Mathematical Theories and Applications · Cosmology and Gravitation Theories