Elements of causality theory
Piotr T. Chru\'sciel

TL;DR
This paper introduces a simplified approach to causality theory using causal curves, focusing on differentiability aspects for twice-continuously-differentiable metrics, offering a coherent but partial treatment of the subject.
Contribution
It presents an original, simplified framework for causality theory based on causal curves, emphasizing differentiability requirements for a coherent mathematical structure.
Findings
Simplified causal curve-based approach to causality theory
Coherent theory developed for twice-continuously-differentiable metrics
Partial but original treatment of causality concepts
Abstract
These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify many arguments. We keep track of the differentiability needed for various statements, obtaining a coherent theory for twice-continuously-differentiable metrics.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Cosmology and Gravitation Theories · Noncommutative and Quantum Gravity Theories
