The causal hierarchy of spacetimes

TL;DR

This paper constructs and updates the causal hierarchy of spacetimes, revisiting foundational concepts, exploring recent developments like smoothability and isocausality, and clarifying the properties of each level in the causal ladder.

Contribution

It provides a comprehensive construction and analysis of the causal hierarchy of spacetimes, incorporating recent solutions and alternative approaches.

Findings

Updated properties of the causal ladder

Revisited concepts with minimal hypotheses

Summarized implications of recent smoothability results

Abstract

The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative proposals (as recent isocausality), are also summarized.