Elements of causality theory

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.